{"id":39791,"date":"2022-04-06T12:45:01","date_gmt":"2022-04-06T07:15:01","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=39791"},"modified":"2022-04-07T11:32:16","modified_gmt":"2022-04-07T06:02:16","slug":"big-ideas-math-algebra-2-answers-chapter-4","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-4\/","title":{"rendered":"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions"},"content":{"rendered":"<p><strong>Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions<\/strong> are aligned based on the latest syllabus and common core curriculum guidelines. Also, you can get a step-by-step explanation by the subject experts for all questions covered in the Big Ideas Math Book Algebra 2 Ch 4 Polynomials Functions Solution Key. Polynomials are a very important concept for high school students to calculate various complex calculations in further chapters. So, it is very crucial to download and practice the questions covered in BIM Textbook solutions of Algebra 2 Ch 4 Polynomial Functions.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 2 Answer Key Chapter 4 Polynomial Functions<\/h2>\n<p>Improving your Math skills is the best way to score high marks and also become a pro in math concepts. Access the available links below and download free pdf formatted<a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers\/\"> Big Ideas Math Algebra 2 Solutions<\/a> of Ch 4 Polynomial functions. This Polynomial functions<strong> Big Ideas Math Book Algebra 2 Ch 4 Answer Key<\/strong> includes questions from 4.1 to 4.9 lessons exercises, assignment tests, practice tests, chapter tests, quizzes, etc. Get a fun learning environment with the help of <span style=\"font-size: 16px;\">BIM Algebra 2 Textbook Answers and practice well by solving the questions given in BIM study materials.\u00a0<\/span><\/p>\n<ul>\n<li><a href=\"#Polynomial_Functions_Maintaining_Mathematical_Proficiency\">Polynomial Functions Maintaining Mathematical Proficiency &#8211; Page 155<\/a><\/li>\n<li><a href=\"#Polynomial_Functions_Mathematical_Practices\">Polynomial Functions Mathematical Practices &#8211; Page 156<\/a><\/li>\n<li><a href=\"#Lesson_4.1_Graphing_Polynomial_Functions\">Lesson 4.1 Graphing Polynomial Functions &#8211; Page (158-164)<\/a><\/li>\n<li><a href=\"#Graphing_Polynomial_Functions_4.1_Exercises\">Graphing Polynomial Functions 4.1 Exercises &#8211; Page(162-164)<\/a><\/li>\n<li><a href=\"#Lesson_4.2_Adding,_Subtracting,_and_Multiplying_Polynomials\">Lesson 4.2 Adding, Subtracting, and Multiplying Polynomials &#8211; Page(166-172)<\/a><\/li>\n<li><a href=\"#Adding,_Subtracting,_and_Multiplying_Polynomials_4.2_Exercises\">Adding, Subtracting, and Multiplying Polynomials 4.2 Exercises &#8211; Page(170-172)<\/a><\/li>\n<li><a href=\"#Lesson_4.3_Dividing_Polynomials\">Lesson 4.3 Dividing Polynomials &#8211; Page(174-178)<\/a><\/li>\n<li><a href=\"#Dividing_Polynomials_4.3_Exercises\">Dividing Polynomials 4.3 Exercises &#8211; Page(177-178)<\/a><\/li>\n<li><a href=\"#Lesson_4.4_Factoring_Polynomials\">Lesson 4.4 Factoring Polynomials &#8211; Page(180-186)<\/a><\/li>\n<li><a href=\"#Factoring_Polynomials_4.4_Exercises\">Factoring Polynomials 4.4 Exercises &#8211; Page(184-186)<\/a><\/li>\n<li><a href=\"#Polynomial_Functions_Study_Skills\">Polynomial Functions Study Skills &#8211; Page 187<\/a><\/li>\n<li><a href=\"#Polynomial_Functions_4.1_-_4.4_Quiz\">Polynomial Functions 4.1 &#8211; 4.4 Quiz &#8211; Page 188<\/a><\/li>\n<li><a href=\"#Lesson_4.5_Solving_Polynomial_Equations\">Lesson 4.5 Solving Polynomial Equations &#8211; Page(190-196)<\/a><\/li>\n<li><a href=\"#Solving_Polynomial_Equations_4.5_Exercises\">Solving Polynomial Equations 4.5 Exercises &#8211; Page(194-196)<\/a><\/li>\n<li><a href=\"#Lesson_4.6_The_Fundamental_Theorem_of_Algebra\">Lesson 4.6 The Fundamental Theorem of Algebra &#8211; Page(198-204)<\/a><\/li>\n<li><a href=\"#The_Fundamental_Theorem_of_Algebra_4.6_Exercises\">The Fundamental Theorem of Algebra 4.6 Exercises &#8211; Page(202-204)<\/a><\/li>\n<li><a href=\"#Lesson_4.7_Transformations_of_Polynomial_Functions\">Lesson 4.7 Transformations of Polynomial Functions &#8211; Page(206-210)<\/a><\/li>\n<li><a href=\"#Transformations_of_Polynomial_Functions_4.7_Exercises\">Transformations of Polynomial Functions 4.7 Exercises &#8211; Page(209-210)<\/a><\/li>\n<li><a href=\"#Lesson_4.8_Analyzing_Graphs_of_Polynomial_Functions\">Lesson 4.8 Analyzing Graphs of Polynomial Functions &#8211; Page(212-218)<\/a><\/li>\n<li><a href=\"#Analyzing_Graphs_of_Polynomial_Functions_4.8_Exercises\">Analyzing Graphs of Polynomial Functions 4.8 Exercises &#8211; Page(216-218)<\/a><\/li>\n<li><a href=\"#Lesson_4.9_Modeling_with_Polynomial_Functions\">Lesson 4.9 Modeling with Polynomial Functions &#8211; Page(220-224)<\/a><\/li>\n<li><a href=\"#Modeling_with_polynomial_Functions_4.9_Exercises\">Modeling with polynomial Functions 4.9 Exercises &#8211; Page(223-224)<\/a><\/li>\n<li><a href=\"#Polynomial_Functions_Performance_Task\">Polynomial Functions Performance Task &#8211; Page 225<\/a><\/li>\n<li><a href=\"#Polynomial_Functions_Chapter_Review\">Polynomial Functions Chapter Review &#8211; Page(226-230)<\/a><\/li>\n<li><a href=\"#Polynomial_Functions_Chapter_Test\">Polynomial Functions Chapter Test &#8211; Page 231<\/a><\/li>\n<li><a href=\"#Polynomial_Functions_Cumulative_Assessment\">Polynomial Functions Cumulative Assessment &#8211; Page(232-233)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Polynomial_Functions_Maintaining_Mathematical_Proficiency\"><\/a>Polynomial Functions Maintaining Mathematical Proficiency<\/h3>\n<p><b>Simplify the expression.<\/b><\/p>\n<p>Question 1.<br \/>\n6x \u2212 4x=2x<\/p>\n<p>Explanation:<\/p>\n<p>Terms can be combined only if they have the exact same variable portion and combining like terms.<\/p>\n<p>Question 2.<br \/>\n12m \u2212 m \u2212 7m + 3<\/p>\n<p>Answer:<\/p>\n<p>12m-m-7m+3<\/p>\n<p>=4m+3<\/p>\n<p>Question 3.<br \/>\n3(y + 2) \u2212 4y<\/p>\n<p>Answer:<\/p>\n<p>3(y+2)-4y<\/p>\n<p>3y+6-4y<\/p>\n<p>-y+6<\/p>\n<p>Question 4.<br \/>\n9x \u2212 4(2x \u2212 1)<\/p>\n<p>Answer:<\/p>\n<p>9x-4(2x-1)<\/p>\n<p>=9x-8x+4<\/p>\n<p>=x+4<\/p>\n<p>Question 5.<br \/>\n\u2212(z + 2) \u2212 2(1 \u2212 z)<\/p>\n<p>Answer:-<\/p>\n<p>= -z-2-2+z<\/p>\n<p>=-4<\/p>\n<p>Question 6.<br \/>\n\u2212x<sup>2<\/sup> + 5x + x<sup>2<\/sup><\/p>\n<p>Answer:<\/p>\n<p>5x<\/p>\n<p><b>Find the volume of the solid.<\/b><\/p>\n<p>Question 7.<br \/>\ncube with side length 4 inches<\/p>\n<p>solution:\u00a0<img loading=\"lazy\" class=\"alignnone wp-image-83138\" style=\"font-weight: inherit;\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/paint-1.png\" alt=\"\" width=\"167\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/paint-1.png 1152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/paint-1-300x169.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/paint-1-1024x576.png 1024w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/paint-1-768x432.png 768w\" sizes=\"(max-width: 167px) 100vw, 167px\" \/><\/p>\n<p>Volume of cube=sidexsidexside<\/p>\n<p>=4x4x4<\/p>\n<p>=64inches<\/p>\n<p>sphere with radius 2 feet<\/p>\n<p>Question 9.<br \/>\nrectangular prism with length 4 feet, width 2 feet, and height 6 feet<\/p>\n<p>Solution: Given that<\/p>\n<p>length= 4 feet<\/p>\n<p>width=2 feet<\/p>\n<p>height= 6 feet<\/p>\n<p>volume of rectangular prism= length x width x height<\/p>\n<p><img loading=\"lazy\" class=\"\" src=\"https:\/\/www.bing.com\/images\/blob?bcid=S3.op4I8oZQCRFaMfm1d49ektLlQ.....8w\" alt=\"See the source image\" width=\"229\" height=\"103\" \/><\/p>\n<p>substitute the values in\u00a0 formula<\/p>\n<p>volume of rectangular prism= 4 x 2 x 6= 48 cubic feet<\/p>\n<p>Question 10.<\/p>\n<p>right cylinder with radius 3 centimeters and height 5 centimeters<\/p>\n<p>Solution:<\/p>\n<p>Given that<\/p>\n<p>radius=3centimeters<\/p>\n<p>height =5centimeter<\/p>\n<p>Volume of a cylinder = area of base \u00d7 height = \u03c0 \u00d7 r<sup>2<\/sup>\u00d7 h and you can use 3.14 for \u03c0.<img loading=\"lazy\" class=\"wp-image-83413 alignleft\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0403_114734.jpg\" alt=\"\" width=\"90\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0403_114734.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0403_114734-245x300.jpg 245w\" sizes=\"(max-width: 90px) 100vw, 90px\" \/><\/p>\n<p>substitute the values in formula<\/p>\n<p>3.14 x 3 x 3 x 5=141.3cubic centimeter<\/p>\n<p>Question 11.<br \/>\n<b>ABSTRACT REASONING<\/b> Does doubling the volume of a cube have the same effect on the side length? Explain your reasoning<\/p>\n<p>Solution:<\/p>\n<p>If the side of the cube id doubled. the volume is 8 times larger\u00a0 .<\/p>\n<p>example: let&#8217;s use a cube that has side lenghts of 2 as an\u00a0 example. the volume of that cube would be lenght x and width x height<\/p>\n<p>2 x 2 x\u00a0 2 =8. if we double the edges to 4 . it would be 4 x 4 x 4, which is 64. to find how many times increases take the 64 and divide by 8 . 64\/8=8 The volume increases by 8 times.<\/p>\n<p>&nbsp;<\/p>\n<h3><a id=\"Polynomial_Functions_Mathematical_Practices\"><\/a>Polynomial Functions Mathematical Practices<\/h3>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Use a graphing calculator to determine whether the function is continuous. Explain your reasoning.<\/b><\/p>\n<p>Question 1.<br \/>\nf(x) = \\(\\frac{x^{2}-x}{x}\\)<\/p>\n<p>Question 2.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 3<\/p>\n<p>Question 3.<br \/>\nf(x) = \\(\\sqrt{x^{2}+1}\\)<\/p>\n<p>Question 4.<br \/>\nf(x) = | x + 2 |<\/p>\n<p>Question 5.<br \/>\nf(x) = \\(\\frac{1}{x}\\)<\/p>\n<p>Question 6.<br \/>\nf(x) = \\(\\frac{1}{\\sqrt{x^{2}-1}}\\)<\/p>\n<p>Question 7.<br \/>\nf(x) = x<\/p>\n<p>Question 8.<br \/>\nf(x) = 2x \u2212 3<\/p>\n<p>Question 9.<br \/>\nf(x) = \\(\\frac{x}{x}\\)<\/p>\n<h3><a id=\"Lesson_4.1_Graphing_Polynomial_Functions\"><\/a>Lesson 4.1 Graphing Polynomial Functions<\/h3>\n<p><b>Essential Question<\/b><br \/>\nWhat are some common characteristics of the graphs of cubic and quartic polynomial functions?<br \/>\nA polynomial function of the form<br \/>\nf(x) = a<sub>n<\/sub>x<sup>n<\/sup> + a<sub>n \u2013 1<\/sub>x<sup>n\u2013 1<\/sup> +. . .+ a<sub>1<\/sub>x + a<sub>0<\/sub><br \/>\nwhere a<sub>n<\/sub> \u2260 0, is cubic when n = 3 and quartic when n = 4.<\/p>\n<p><b>EXPLORATION 1<br \/>\nIdentifying Graphs of Polynomial Functions<br \/>\nWork with a partner.<\/b> Match each polynomial function with its graph. Explain your reasoning. Use a graphing calculator to verify your answers.<br \/>\na. f(x) = x<sup>3<\/sup> \u2212 x<br \/>\nb. f(x) = \u2212x<sup>3<\/sup> + x<br \/>\nc. f(x) = \u2212x<sup>4<\/sup> + 1<br \/>\nd. f(x) = x<sup>4<\/sup><br \/>\ne. f(x) = x<sup>3<\/sup><br \/>\nf. f(x) = x<sup>4<\/sup> \u2212 x<sup>2<\/sup><\/p>\n<p><b>EXPLORATION 2<br \/>\nIdentifying x-Intercepts of Polynomial Graphs<br \/>\nWork with a partner.<\/b> Each of the polynomial graphs in Exploration 1 has x-intercept(s) of \u22121, 0, or 1. Identify the x-intercept(s) of each graph. Explain how you can verify your answers.<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nWhat are some common characteristics of the graphs of cubic and quartic polynomial functions?<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 1\" width=\"258\" height=\"196\" \/><br \/>\nDetermine whether each statement is true or false. Justify your answer.<br \/>\na. When the graph of a cubic polynomial function rises to the left, it falls to the right.<br \/>\nb. When the graph of a quartic polynomial function falls to the left, it rises to the right.<\/p>\n<p><b>4.1 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.<\/b><\/p>\n<p>Question 1.<br \/>\nf(x) = 7 \u2212 1.6x<sup>2<\/sup> \u2212 5x<\/p>\n<p>Answer:<\/p>\n<p>The standard form of a polynomials has the exponents of the terms arranged in descending order.<\/p>\n<p>The \u00a0degree of a polynomial is the highest exponent of a term.<\/p>\n<p>The type of a polynomial depends on the degree.<\/p>\n<p>The leading coefficient is the numerical factor of the terms with highest degree.<\/p>\n<p>Hence the given function f(x) = 7 \u2212 1.6x<sup>2<\/sup> \u2212 5x has the\u00a0 following characteristic<\/p>\n<p>Standard form f (x) = -1.6x<sup>2 <\/sup>-5x +7<\/p>\n<p>Degree: 2<\/p>\n<p>Type: quadratic<\/p>\n<p>Leading coefficient: -1.6<\/p>\n<p>Question 2.<br \/>\np(x) =x+ 2x<sup>-2<\/sup> + 9.5<\/p>\n<p>Answer:<\/p>\n<p>The function is not a polynomial function because the term 2x<sup>-2<\/sup> has an exponent\u00a0 that is not a whole number<\/p>\n<p>Question 3.<br \/>\nq(x) = x<sup>3<\/sup> \u2212 6x + 3x<sup>4<\/sup><\/p>\n<p>Answer:<\/p>\n<p>The standard form of a polynomials has the exponents of the terms arranged in descending order.<\/p>\n<p>The \u00a0degree of a polynomial is the highest exponent of a term.<\/p>\n<p>The type of a polynomial depends on the degree.<\/p>\n<p>The leading coefficient is the numerical factor of the terms with highest degree.<\/p>\n<p>Hence the given function q(x) = x<sup>3<\/sup> \u2212 6x + 3x<sup>4<\/sup> \u00a0has the\u00a0 following characteristic<\/p>\n<p>Standard form : q(x) = 3x<sup>4<\/sup> + x<sup>3<\/sup> &#8211; 6x<\/p>\n<p>Degree: 4<\/p>\n<p>Type: quadratic<\/p>\n<p>Leading coefficient: 3<\/p>\n<p>&nbsp;<\/p>\n<p><b>Evaluate the function for the given value of x.<\/b><\/p>\n<p>Question 4.<br \/>\nf(x) = \u2212x<sup>3<\/sup> + 3x<sup>2<\/sup> + 9; x = 4<\/p>\n<p>Answer:<\/p>\n<p>f(x) = \u2212x<sup>3<\/sup> + 3x<sup>2<\/sup> + 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Write Original equation<\/p>\n<p>f(4) =\u2212x<sup>3<\/sup> + 3x<sup>2<\/sup> + 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 substitute for x<\/p>\n<p>=-(4)<sup>3<\/sup>+ 3(4)<sup>2 <\/sup>+9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Evaluate powers and multiply<\/p>\n<p>=-(64)+ 3(16) +9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Simplify<\/p>\n<p>=-64 + 48 + 9<\/p>\n<p>=-7<\/p>\n<p>Question 5.<br \/>\nf(x) = 3x<sup>5<\/sup> \u2212 x<sup>4<\/sup> \u2212 6x + 10; x = \u22122<\/p>\n<p>Answer:<\/p>\n<p>f(x) = 3x<sup>5<\/sup> \u2212 x<sup>4<\/sup> \u2212 6x + 10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Write Original equation<\/p>\n<p>f(-2)=3(-2)<sup>5<\/sup>-(-2)<sup>4<\/sup>-6(-2)+10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 substitute for x<\/p>\n<p>=3(-32)-16+12+10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Evaluate powers and multiply<\/p>\n<p>= -96 -16 +12 +10\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Simplify<\/p>\n<p>=-90<\/p>\n<p>Question 6.<br \/>\nDescribe the end behavior of the graph of f(x) = 0.25x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 1.<\/p>\n<p><b>Graph the polynomial Function<\/b><\/p>\n<p>Question 7.<br \/>\nf(x) = x<sup>4<\/sup> + x<sup>2<\/sup> \u2212 3<\/p>\n<p>Question 8.<br \/>\nf(x) = 4 \u2212 x<sup>3<\/sup><\/p>\n<p>Question 9.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + x \u2212 1<\/p>\n<p>Question 10.<br \/>\nSketch a graph of the polynomial function f having these characteristics.<\/p>\n<ul>\n<li>f is decreasing when x &lt; \u22121.5 and x &gt; 2.5; f is increasing when \u22121.5 &lt; x &lt; 2.5.<\/li>\n<li><span style=\"font-size: 16px;\">f(x) &gt; 0 when x &lt; \u22123 and 1 &lt; x &lt; 4; f(x) &lt; 0 when \u22123 &lt; x &lt; 1 and x &gt; 4.<\/span><\/li>\n<\/ul>\n<p><b>Use the graph to describe the degree and leading coefficient of f.<\/b><\/p>\n<p>Question 11.<br \/>\n<b>WHAT IF?<\/b> Repeat Example 6 using the alternative model for electric vehicles of<br \/>\nV(t) = \u22120.0290900t<sup>4<\/sup> + 0.791260t<sup>3<\/sup> \u2212 7.96583t<sup>2<\/sup> + 36.5561t \u2212 12.025.<\/p>\n<h3><a id=\"Graphing_Polynomial_Functions_4.1_Exercises\"><\/a>Graphing Polynomial Functions 4.1 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b> Explain what is meant by the end behavior of a polynomial function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 1\" width=\"556\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-1.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-1-300x46.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WHICH ONE DOESN\u2019T BELONG?<\/b> Which function does not belong with the other three? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 2\" width=\"477\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-2.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-2-300x75.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u20138, decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = \u22123x + 5x<sup>3<\/sup> \u2212 6x<sup>2<\/sup> + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 3\" width=\"570\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-3.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-3-300x45.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 4.<br \/>\np(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 3x \u2212 4x<sup>3<\/sup> + 6x<sup>4<\/sup> \u2212 1<br \/>\nAnswer:<\/p>\n<p>The function is a polynomial function . Written in standard form , the function is p(x)=1\/2 x<sup>2<\/sup> + 3x \u2212 4x<sup>3<\/sup> + 6x<sup>4<\/sup> \u2212 1\u00a0 \u00a0.<\/p>\n<p>It has degree 4(quartic)\u00a0 \u00a0and leading coefficient of 6.<\/p>\n<p>&nbsp;<\/p>\n<p>Question 5.<br \/>\nf(x) = 9x<sup>4<\/sup> + 8x<sup>3<\/sup> \u2212 6x<sup>-2<\/sup> + 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 5\" width=\"541\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-5.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-5-300x33.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 6.<br \/>\ng(x) = \\(\\sqrt{3}\\) \u2212 12x + 13x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nh(x) = \\(\\frac{5}{3}\\)x<sup>2<\/sup> \u2212 \\(\\sqrt{7}\\)x<sup>4<\/sup> + 8x<sup>3<\/sup> \u2212 \\(\\frac{1}{2}\\) + x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 7\" width=\"550\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-7.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-7-300x49.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 8.<br \/>\nh(x) = 3x<sup>4<\/sup> + 2x \u2212 \\(\\frac{5}{x}\\) + 9x<sup>3<\/sup> \u2212 7<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 9 and 10, describe and correct the error in analyzing the function.<\/b><\/p>\n<p>Question 9.<br \/>\nf(x) = 8x<sup>3<\/sup> \u2212 7x<sup>4<\/sup> \u2212 9x \u2212 3x<sup>2<\/sup> + 11<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 3\" width=\"376\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-3.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-3-300x78.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 9\" width=\"560\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-9.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-9-300x62.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = 2x<sup>4<\/sup> + 4x &#8211; 9\\(\\sqrt{x}\\) + 3x<sup>2<\/sup> &#8211; 8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4\" width=\"377\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4-300x73.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 11\u201316, evaluate the function for the given value of x.<\/b><\/p>\n<p>Question 11.<br \/>\nh(x) = \u22123x<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 12x \u2212 6; x = \u22122<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 11\" width=\"416\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-11.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-11-300x95.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 12.<br \/>\nf(x) = 7x<sup>4<\/sup> \u2212 10x<sup>2<\/sup> + 14x \u2212 26; x = \u22127<\/p>\n<p>Answer:<\/p>\n<p>f(x) = 7x<sup>4<\/sup> \u2212 10x<sup>2<\/sup> + 14x \u2212 26\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Write Original equation<\/p>\n<p>f(-7)\u00a0 \u00a0 \u00a0=\u00a0 7(-7)<sup>4<\/sup>&#8211; 10(-7)<sup>2<\/sup>+14(-7)-26\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0substitute for x<\/p>\n<p>= 7(2401)- 10(49)- 98-26\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Evaluate powers and multiply<\/p>\n<p>= 16807- 490- 98- 26\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Simplify<\/p>\n<p>= 16,193<\/p>\n<p>Question 13.<br \/>\ng(x) = x<sup>6<\/sup> \u2212 64x<sup>4<\/sup> + x<sup>2<\/sup> \u2212 7x \u2212 51; x = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 13\" width=\"415\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-13.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-13-300x96.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p>Question 14.<br \/>\ng(x) = \u2212x<sup>3<\/sup> + 3x<sup>2<\/sup> + 5x + 1; x = \u221212<\/p>\n<p>Answer:<\/p>\n<p>g(x) = \u2212x<sup>3<\/sup> + 3x<sup>2<\/sup> + 5x + 1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Write Original equation<\/p>\n<p>g(-12) =(-12 )<sup>3<\/sup>+ 3(-12) <sup>2<\/sup>+ 5(-12 )+1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 substitute for x<\/p>\n<p>=1728 + 3(144) &#8211; 60 +1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Evaluate powers and multiply<\/p>\n<p>=1728 + 432 &#8211; 60 +1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Simplify<\/p>\n<p>=2101<\/p>\n<p>Question 15.<br \/>\np(x) = 2x<sup>3<\/sup> + 4x<sup>2<\/sup> + 6x + 7; x = \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 15\" width=\"320\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-15.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-15-300x151.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Question 16.<\/p>\n<p>h(x) = 5x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + 2x + 4; x = \u221212<\/p>\n<p>Answer:<br \/>\nh(x) = 5x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + 2x + 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Write Original equation<\/p>\n<p>h(-12)\u00a0 \u00a0 =5(-12)<sup>3<\/sup>-3(-12)<sup>2<\/sup>+2(-12)+4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 substitute for x<\/p>\n<p>=5(-1728)-3(144)-24+4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0Evaluate powers and multiply<\/p>\n<p>=-8640-432-24+4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0Simplify<\/p>\n<p>=-9092<\/p>\n<p><b>In Exercises 17\u201320, describe the end behavior of the graph of the function.<\/b><\/p>\n<p>Question 17.<br \/>\nh(x) = \u22125x<sup>4<\/sup> + 7x<sup>3<\/sup> \u2212 6x<sup>2<\/sup> + 9x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 17\" width=\"626\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-17.png 626w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-17-300x42.png 300w\" sizes=\"(max-width: 626px) 100vw, 626px\" \/><\/p>\n<p>Question 18.<br \/>\ng(x) = 7x<sup>7<\/sup> + 12x<sup>5<\/sup> \u2212 6x<sup>3<\/sup> \u2212 2x \u2212 18<\/p>\n<p>Answer:<\/p>\n<p>The function as degree 7 and leading coefficient 7 . Because the\u00a0 degree is odd and leading coefficient \u00a0is positive g(x)-&gt;-\u221e as x -&gt;-\u221e\u00a0 and\u00a0 g(x)-&gt;+\u221e as x-&gt;+\u221e<\/p>\n<p>Question 19.<br \/>\nf(x) = \u22122x<sup>4<\/sup> + 12x<sup>8<\/sup> + 17 + 15x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 19\" width=\"621\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-19.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-19-300x41.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p>Question 20.<br \/>\nf(x) = 11 \u2212 18x<sup>2<\/sup> \u2212 5x<sup>5<\/sup> \u2212 12x<sup>4<\/sup> \u2212 2x<br \/>\nAnswer:<\/p>\n<p>f(x)= \u2212 5x<sup>5<\/sup> \u2212 12x<sup>4<\/sup>\u2212 18x<sup>2<\/sup>\u2212 2x + 11<\/p>\n<p>with the highest exponent is equal to 5, then the polynomial is of odd degree.<\/p>\n<p>Hence the end behaviors are opposite. With the negative leading coefficient<\/p>\n<p>Then \u00a0\u00a0f(x) \u2500&gt; \u221e as x \u2500&gt;-\u221e<\/p>\n<p>f(x)\u2500&gt;-\u221e as \u00a0x \u2500&gt;+\u221e<\/p>\n<p>&nbsp;<\/p>\n<p><b>In Exercises 21 and 22, describe the degree and leading coefficient of the polynomial function using the graph.<\/b><\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 5\" width=\"161\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-5.png 161w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-5-150x150.png 150w\" sizes=\"(max-width: 161px) 100vw, 161px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 21\" width=\"546\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-21.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-21-300x47.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 6\" width=\"168\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-6.png 168w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-6-150x150.png 150w\" sizes=\"(max-width: 168px) 100vw, 168px\" \/><br \/>\nAnswer:<\/p>\n<p>The degree of the polynomial is even since one side goes up and other goes up; the leading coefficient is positive\u00a0 since the left side goes up and the right side goes up.<\/p>\n<p>Question 23.<br \/>\n<b>USING STRUCTURE<\/b> Determine whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.<br \/>\nf(x) = 5x<sup>3<\/sup>x + \\(\\frac{5}{2}\\)x<sup>3<\/sup> \u2212 9x<sup>4<\/sup> + \\(\\sqrt{2}\\)x<sup>2<\/sup> + 4x \u2212 1 \u2212 x<sup>-5<\/sup>x<sup>5<\/sup> \u2212 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 23\" width=\"560\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-23.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-23-300x46.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 24.<br \/>\n<b>WRITING<\/b> Let f(x) = 13. State the degree, type, and leading coefficient. Describe the end behavior of the function. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 25\u201332, graph the polynomial function.<\/b><\/p>\n<p>Question 25.<br \/>\np(x) = 3 \u2212 x<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47576\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 25\" width=\"657\" height=\"494\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-25.png 657w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-25-300x226.png 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><\/p>\n<p>Question 26.<br \/>\ng(x) = x<sup>3<\/sup> + x + 3<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nf(x) = 4x \u2212 9 \u2212 x<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47577\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 27\" width=\"584\" height=\"537\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-27.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-27-300x276.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 28.<br \/>\np(x) = x<sup>5<\/sup> \u2212 3x<sup>3<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nh(x) = x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> + 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47578\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 29\" width=\"578\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-29.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-29-300x256.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 30.<br \/>\nh(x) = 5 + 3x<sup>2<\/sup> \u2212 x<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ng(x) = x<sup>5<\/sup> \u2212 3x<sup>4<\/sup> + 2x \u2212 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 31\" width=\"571\" height=\"580\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-31.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-31-295x300.png 295w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 32.<br \/>\np(x) = x<sup>6<\/sup> \u2212 2x<sup>5<\/sup> \u2212 2x<sup>3<\/sup> + x + 5<br \/>\nAnswer:<\/p>\n<p><b>ANALYZING RELATIONSHIPS In Exercises 33\u201336, describe the x-values for which<br \/>\n(a) f is increasing or decreasing,<br \/>\n(b) f(x) &gt; 0, and<br \/>\n(c) f(x) &lt; 0.<\/b><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 7\" width=\"159\" height=\"167\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 33\" width=\"579\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-33.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-33-300x65.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 8\" width=\"168\" height=\"165\" \/><br \/>\nAnswer:<\/p>\n<p>a. The function is increases\u00a0 when x&lt; 4 and decreases when x&gt;4.<\/p>\n<p>b.The function is positive when x&lt;<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 9\" width=\"163\" height=\"168\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 35\" width=\"562\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-35.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-35-300x68.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-10.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 10\" width=\"165\" height=\"168\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 37\u201340, sketch a graph of the polynomial function f having the given characteristics. Use the graph to describe the degree and leading coefficient of the function f.<\/b><\/p>\n<p>Question 37.<\/p>\n<ul>\n<li>f is increasing when x &gt; 0.5; f is decreasing when x &lt; 0.5.<\/li>\n<li>f(x) &gt; 0 when x &lt; \u22122 and x &gt; 3; f(x) &lt; 0 when \u22122 &lt; x &lt; 3.<\/li>\n<\/ul>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 37\" width=\"548\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-37.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-37-300x193.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 38.<\/p>\n<ul>\n<li>f is increasing when \u22122 &lt; x &lt; 3;f is decreasing when x &lt; \u22122 and x &gt; 3.<\/li>\n<li>f(x) &gt; 0 when x &lt; \u22124 and 1 &lt; x &lt; 5; f(x) &lt; 0 when \u22124 &lt; x &lt; 1 and x &gt; 5.<\/li>\n<\/ul>\n<p>Answer:<br \/>\nQuestion 39.<\/p>\n<ul>\n<li>f is increasing when \u22122 &lt; x &lt; 0 and x &gt; 2;f is decreasing when x &lt; \u22122 and 0 &lt; x &lt; 2.<\/li>\n<li>f(x) &gt; 0 when x &lt; \u22123, \u22121 &lt; x &lt; 1, and x &gt; 3; f(x) &lt; 0 when \u22123 &lt; x &lt; \u22121 and 1 &lt; x &lt; 3.<\/li>\n<\/ul>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 39\" width=\"542\" height=\"445\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-39.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-39-300x246.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 40.<\/p>\n<ul>\n<li>f is increasing when x &lt; \u22121 and x &gt; 1;f is decreasing when \u22121 &lt; x &lt; 1.<\/li>\n<li>f(x) &gt; 0 when \u22121.5 &lt; x &lt; 0 and x &gt; 1.5; f(x) &lt; 0 when x &lt; \u22121.5 and 0 &lt; x &lt; 1.5.<\/li>\n<\/ul>\n<p>Answer:<br \/>\nQuestion 41.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> From 1980 to 2007 the number of drive-in theaters in the United States can be modeled by the function<br \/>\nd(t) = \u22120.141t<sup>3<\/sup> + 9.64t<sup>2<\/sup> \u2212 232.5t + 2421<br \/>\nwhere d(t) is the number of open theaters and t is the number of years after 1980.<br \/>\na. Use a graphing calculator to graph the function for the interval 0 \u2264 t \u2264 27. Describe the behavior of the graph on this interval.<br \/>\nb. What is the average rate of change in the number of drive-in movie theaters from 1980 to 1995 and from 1995 to 2007? Interpret the average rates of change.<br \/>\nc. Do you think this model can be used for years before 1980 or after 2007? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 11\" width=\"290\" height=\"165\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47584\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-41.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 41.1\" width=\"603\" height=\"641\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-41.1.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-41.1-282x300.png 282w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-41.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 41.2\" width=\"581\" height=\"366\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-41.2.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-41.2-300x189.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>PROBLEM SOLVING<\/b> The weight of an ideal round-cut diamond can be modeled by<br \/>\nw = 0.00583d<sup>3<\/sup> \u2212 0.0125d<sup>2<\/sup> + 0.022d \u2212 0.01<br \/>\nwhere w is the weight of the diamond (in carats) and d is the diameter (in millimeters). According to the model, what is the weight of a diamond with a diameter of 12 millimeters?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-12.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 12\" width=\"166\" height=\"137\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<b>ABSTRACT REASONING<\/b> Suppose f(x) \u2192 \u221e as x \u2192 \u2212\u221e and f(x) \u2192\u2212\u221e as x \u2192 \u221e. Describe the end behavior of g(x) = \u2212f(x). Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47586\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 43\" width=\"547\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-43.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-43-300x60.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 44.<br \/>\n<b>THOUGHT PROVOKING<\/b> Write an even degree polynomial function such that the end behavior of f is given by f(x) \u2192 \u2212\u221e as x \u2192 \u2212\u221e and f(x) \u2192 \u2212\u221e as x \u2192 \u221e. Justify your answer by drawing the graph of your function.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<b>USING TOOLS<\/b> When using a graphing calculator to graph a polynomial function, explain how you know when the viewing window is appropriate.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47587\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 45\" width=\"573\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-45.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-45-300x30.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend uses the table to speculate that the function f is an even degree polynomial and the function g is an odd degree polynomial. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 13\" width=\"265\" height=\"197\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>DRAWING CONCLUSIONS<\/b> The graph of a function is symmetric with respect to the y-axis if for each point (a, b) on the graph, (\u2212a, b) is also a point on the graph. The graph of a function is symmetric with respect to the origin if for each point (a, b) on the graph, (\u2212a, \u2212b) is also a point on the graph.<br \/>\na. Use a graphing calculator to graph the function y = x<sup>n<\/sup> when n = 1, 2, 3, 4, 5, and 6. In each case, identify the symmetry of the graph.<br \/>\nb. Predict what symmetry the graphs of y = x<sup>10<\/sup> and y = x<sup>11<\/sup> each have. Explain your reasoning and then confirm your predictions by graphing.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-47.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 47.1\" width=\"547\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-47.1.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-47.1-300x287.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47589\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-47.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 47.2\" width=\"594\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-47.2.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-47.2-300x112.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> The graph of a polynomial function is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-14.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 14\" width=\"226\" height=\"217\" \/><br \/>\na. Describe the degree and leading coefficient of f.<br \/>\nb. Describe the intervals where the function is increasing and decreasing.<br \/>\nc. What is the constant term of the polynomial function?<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>REASONING <\/b>A cubic polynomial function f has a leading coefficient of 2 and a constant term of \u22125. When f(1) = 0 and f(2) = 3, what is f(\u22125)? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47590\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 49\" width=\"580\" height=\"301\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-49.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-49-300x156.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>CRITICAL THINKING<\/b> The weight y (in pounds) of a rainbow trout can be modeled by y = 0.000304x<sup>3<\/sup>, where x is the length (in inches) of the trout.<br \/>\na. Write a function that relates the weight y and length x of a rainbow trout when y is measured in kilograms and x is measured in centimeters. Use the fact that 1 kilogram \u2248 2.20 pounds and 1 centimeter \u2248 0.394 inch.<br \/>\nb. Graph the original function and the function from part (a) in the same coordinate plane. What type of transformation can you apply to the graph of y = 0.000304x<sup>3<\/sup> to produce the graph from part (a)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 15\" width=\"271\" height=\"180\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong> (Skills Review Handbook)<\/p>\n<p>Question 51.<br \/>\nxy + x<sup>2<\/sup> + 2xy + y<sup>2<\/sup> \u2212 3x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47591\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 51\" width=\"527\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-51.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-51-300x38.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Question 52.<br \/>\n2h<sup>3<\/sup>g + 3hg<sup>3<\/sup> + 7h<sup>2<\/sup>g<sup>2<\/sup> + 5h<sup>3<\/sup>g+ 2hg<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n\u2212wk + 3kz \u2212 2kw + 9zk \u2212 kw<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 53\" width=\"357\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-53.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-53-300x84.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p>Question 54.<br \/>\na<sup>2<\/sup>(m \u2212 7a<sup>3<\/sup>) \u2212 m(a<sup>2<\/sup> \u2212 10)<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n3x(xy \u2212 4) + 3(4xy + 3) \u2212 xy(x<sup>2<\/sup>y \u2212 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.1 Question 55\" width=\"432\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-55.png 432w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.1-Question-55-300x118.png 300w\" sizes=\"(max-width: 432px) 100vw, 432px\" \/><\/p>\n<p>Question 56.<br \/>\ncv(9 \u2212 3c) + 2c(v \u2212 4c) + 6c<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_4.2_Adding,_Subtracting,_and_Multiplying_Polynomials\"><\/a>Lesson 4.2 Adding, Subtracting, and Multiplying Polynomials<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you cube a binomial?<\/p>\n<p><b>EXPLORATION 1<br \/>\nCubing Binomials<br \/>\nWork with a partner. <\/b>Find each product. Show your steps.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-16.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 16\" width=\"621\" height=\"491\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-16.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-16-300x237.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nGeneralizing Patterns for Cubing a Binomial<br \/>\nWork with a partner.<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 17\" width=\"256\" height=\"175\" \/><br \/>\na. Use the results of Exploration 1 to describe a pattern for the coefficients of the terms when you expand the cube of a binomial. How is your pattern related to Pascal\u2019s Triangle, shown at the right?<br \/>\nb. Use the results of Exploration 1 to describe a pattern for the exponents of the terms in the expansion of a cube of a binomial.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-18.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 18\" width=\"169\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-18.png 169w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-18-150x150.png 150w\" sizes=\"(max-width: 169px) 100vw, 169px\" \/><br \/>\nc. Explain how you can use the patterns you described in parts (a) and (b) to find the product (2x \u2212 3)<sup>3<\/sup>. Then find this product.<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you cube a binomial?<\/p>\n<p>Question 4.<br \/>\nFind each product.<br \/>\na. (x + 2)<sup>3<\/sup><br \/>\nb. (x \u2212 2)<sup>3<\/sup><br \/>\nc. (2x \u2212 3)<sup>3<\/sup><br \/>\nd. (x \u2212 3)<sup>3<\/sup><br \/>\ne. (\u22122x + 3)<sup>3<\/sup><br \/>\nf. (3x \u2212 5)<sup>3<\/sup><\/p>\n<p><b>4.2 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Find the sum or difference.<\/b><\/p>\n<p>Question 1.<br \/>\n(2x<sup>2<\/sup> \u2212 6x + 5) + (7x<sup>2<\/sup> \u2212 x \u2212 9)<\/p>\n<p>Answer:<\/p>\n<p>Removing the\u00a0 grouping symbols and combining the like terms, the given expression is<\/p>\n<p>(2x<sup>2<\/sup> \u2212 6x + 5) + (7x<sup>2<\/sup> \u2212 x \u2212 9), is equivalent to<\/p>\n<p>=\u00a0\u00a0\u00a0\u00a0 \u00a02x<sup>2<\/sup> \u2212 6x + 5 + 7x<sup>2<\/sup> \u2212 x \u2212 9<\/p>\n<p>=\u00a0\u00a0 (2x<sup>2<\/sup>+7x<sup>2<\/sup>)+( \u2212 6x\u2212 x)+( 5-9)<\/p>\n<p>=\u00a0\u00a0 9x<sup>2<\/sup>-7x-4<\/p>\n<p>Question 2.<br \/>\n(3t<sup>3<\/sup> + 8t<sup>2<\/sup> \u2212 t \u2212 4) \u2212 (5t<sup>3<\/sup> \u2212 t<sup>2<\/sup> + 17)<\/p>\n<p>Answer:<\/p>\n<p>(3t<sup>3<\/sup> + 8t<sup>2<\/sup> \u2212 t \u2212 4) \u2212 (5t<sup>3<\/sup> \u2212 t<sup>2<\/sup> + 17)<\/p>\n<p>=3t<sup>3 <\/sup>+8t<sup>2 <\/sup>-t- 4- 5t<sup>3 <\/sup>+ t<sup>2 <\/sup>-17\u00a0 \u00a0 \u00a0(write the opposite of the subtracted polynomial, then add like terms)<\/p>\n<p>=\u00a0 -2t<sup>3<\/sup>+ 9t<sup>2 <\/sup>-t -21<\/p>\n<p><b>Find the product.<\/b><\/p>\n<p>Question 3.<br \/>\n(4x<sup>2<\/sup> + x \u2212 5)(2x + 1)<\/p>\n<p>Answer:<\/p>\n<p>(4x<sup>2<\/sup> + x \u2212 5)(2x + 1)<\/p>\n<p>=4x<sup>2<\/sup>(2x+1) + x(2x+1) &#8211; 5(2x+1)\u00a0 \u00a0(we multiply the polynomials in horizontal format)<\/p>\n<p>=8x<sup>3<\/sup>+ 4x<sup>2<\/sup>+ 2x<sup>2<\/sup>+ x- 10x -5<\/p>\n<p>=8x<sup>3<\/sup>+ 6x<sup>2<\/sup>&#8211; 9x -x<\/p>\n<p>Question 4.<br \/>\n(y \u2212 2)(5y<sup>2<\/sup> + 3y \u2212 1)<\/p>\n<p>Answer:<\/p>\n<p>(y \u2212 2)(5y<sup>2<\/sup> + 3y \u2212 1)<\/p>\n<p>=(y-2)5y<sup>2<\/sup>+ (y-2)3y &#8211; (y-2)\u00a0\u00a0\u00a0 (we multiply the polynomials in horizontal format)<\/p>\n<p>=5y<sup>3<\/sup>-10y<sup>2<\/sup>+3y<sup>3<\/sup>-6y-y+2<\/p>\n<p>=5y<sup>3<\/sup>-7y<sup>2<\/sup>-7y+2<\/p>\n<p>Question 5.<br \/>\n(m \u2212 2)(m \u2212 1)(m + 3)<\/p>\n<p>Answer:<\/p>\n<p>(m \u2212 2)(m \u2212 1)(m + 3)<\/p>\n<p>=(m<sup>2<\/sup>-m-2m+2)(m+3)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0(we multiply the first two polynomial in horizontal format , then the result<\/p>\n<p>=(m<sup>2<\/sup>-3m+2)(m+3)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 by the last polynomial )<\/p>\n<p>=(m<sup>2<\/sup>-3m+2)m+(m<sup>2<\/sup>-3m+2)3<\/p>\n<p>=m<sup>3<\/sup>-3m<sup>2<\/sup>+2m+3m<sup>2<\/sup>-9m+6<\/p>\n<p>=m<sup>3<\/sup>-7m+6<\/p>\n<p>Question 6.<br \/>\n(3t \u2212 2)(3t + 2)<\/p>\n<p>Answer:<\/p>\n<p>(3t \u2212 2)(3t + 2)<\/p>\n<p>we can use the formula: a<sup>2<\/sup>-b<sup>2<\/sup>= (a+ b) (a-b)<\/p>\n<p>=(3t)<sup>2<\/sup>-2<sup>2<\/sup><\/p>\n<p>=9t<sup>2<\/sup>-4<\/p>\n<p>Question 7.<br \/>\n(5a + 2)<sup>2<\/sup><\/p>\n<p>Answer:<\/p>\n<p>(5a + 2)<sup>2<\/sup><\/p>\n<p>=(5a)<sup>2<\/sup>+2. 5a .2+2<sup>2<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ( we can use the formula : (a+ b)<sup>2<\/sup> = a<sup>2<\/sup>+2ab+b<sup>2<\/sup>)<\/p>\n<p>=25a<sup>2<\/sup>+20a+4<\/p>\n<p>Question 8.<\/p>\n<p>(xy \u2212 3)<sup>3<\/sup><\/p>\n<p>Answer:<\/p>\n<p>(xy-3)<sup>3<\/sup><\/p>\n<p>=(x y)<sup>3<\/sup>-3(x y)<sup>2<\/sup>.3+3. xy.3<sup>2<\/sup>-3<sup>3<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ( we can use the formula:(a-b)<sup>3<\/sup>=a<sup>3<\/sup>-3a<sup>2<\/sup> b +3a b <sup>2<\/sup>-b<sup>3<\/sup><\/p>\n<p>=x<sup>3<\/sup>y<sup>3<\/sup>&#8211; 9x <sup>2<\/sup>y<sup>2<\/sup>+27xy-27<\/p>\n<p>Question 9.<br \/>\n(a) Prove the polynomial identity for the cube of a binomial representing a difference: (a \u2212 b)<sup>3<\/sup> = a<sup>3<\/sup> \u2212 3a<sup>2<\/sup>b + 3ab<sup>2<\/sup> \u2212 b<sup>3<\/sup>.<br \/>\n(b) Use the cube of a binomial in part (a) to calculate 9<sup>3<\/sup>.<\/p>\n<p>Answer:<\/p>\n<p>(a) . (a-b)<sup>3<\/sup> =a<sup>3<\/sup>&#8211; 3a <sup>2<\/sup>b+3ab<sup>2<\/sup>-b<sup>3<\/sup>\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0We have to prove the identity:<\/p>\n<p>=\u00a0 \u00a0(a-b)<sup>3<\/sup> =(a-b)(a-b)(a-b)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0We start from left side:<\/p>\n<p>=\u00a0 \u00a0 \u00a0(a<sup>2<\/sup>-2ab+b<sup>2<\/sup>)(a-b)<\/p>\n<p>=\u00a0 \u00a0 a<sup>3<\/sup>-a <sup>2<\/sup>b-2a <sup>2<\/sup>b+2ab<sup>2<\/sup> +ab <sup>2<\/sup>-b<sup>3<\/sup><\/p>\n<p>=\u00a0 \u00a0 a <sup>3<\/sup>-3a <sup>2<\/sup>b+3ab <sup>2<\/sup>&#8211; b<sup>3<\/sup><\/p>\n<p>(b). 9<sup>3<\/sup>=(10-1)<sup>3<\/sup>=10<sup>3<\/sup>-3.10<sup>2<\/sup>.1+3.10.1<sup>2<\/sup>-1<sup>3\u00a0 \u00a0 \u00a0\u00a0<\/sup><\/p>\n<p>= 1000-300+30-1\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 We use the above identity to compute 9<sup>3<\/sup><\/p>\n<p>= 729<\/p>\n<p>Question 10.<br \/>\nUse Pascal\u2019s Triangle to expand<br \/>\n(a) (z + 3)<sup>4<\/sup> and<br \/>\n(b) (2t \u2212 1)<sup>5<\/sup><\/p>\n<h3><a id=\"Adding,_Subtracting,_and_Multiplying_Polynomials_4.2_Exercises\"><\/a>Adding, Subtracting, and Multiplying Polynomials 4.2 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b> Describe three different methods to expand (x + 3)<sup>3<\/sup>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 1\" width=\"538\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-1.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-1-300x48.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING<\/b> Is (a + b)(a \u2212 b) = a<sup>2<\/sup> \u2212 b<sup>2<\/sup> an identity? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u20138, find the sum.<\/b><\/p>\n<p>Question 3.<br \/>\n(3x<sup>2<\/sup> + 4x \u2212 1) + (\u22122x<sup>2<\/sup> \u2212 3x + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47595\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 3\" width=\"355\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-3.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-3-300x84.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p>Question 4.<br \/>\n(\u22125x<sup>2<\/sup> + 4x \u2212 2) + (\u22128x<sup>2<\/sup> + 2x + 1)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n(12x<sup>5<\/sup> \u2212 3x<sup>4<\/sup> + 2x \u2212 5) + (8x<sup>4<\/sup> \u2212 3x<sup>3<\/sup> + 4x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 5\" width=\"486\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-5.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-5-300x62.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 6.<br \/>\n(8x<sup>4<\/sup> + 2x<sup>2<\/sup> \u2212 1) + (3x<sup>3<\/sup> \u2212 5x<sup>2<\/sup> + 7x + 1)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n(7x<sup>6<\/sup> + 2x<sup>5<\/sup> \u2212 3x<sup>2<\/sup> + 9x) + (5x<sup>5<\/sup> + 8x<sup>3<\/sup> \u2212 6x<sup>2<\/sup> + 2x \u2212 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 7\" width=\"545\" height=\"98\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-7.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-7-300x54.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 8.<br \/>\n(9x<sup>4<\/sup> \u2212 3x<sup>3<\/sup> + 4x<sup>2<\/sup> + 5x + 7) + (11x<sup>4<\/sup> \u2212 4x<sup>2<\/sup> \u2212 11x \u2212 9)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 9\u201314, find the difference.<\/b><\/p>\n<p>Question 9.<br \/>\n(3x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> + 4x \u2212 8) \u2212 (5x<sup>3<\/sup> + 12x<sup>2<\/sup> \u2212 3x \u2212 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47598\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 9\" width=\"485\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-9.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-9-300x62.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 10.<br \/>\n(7x<sup>4<\/sup> \u2212 9x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> + 5x + 6) \u2212 (2x<sup>4<\/sup> + 3x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + x \u2212 4)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n(5x<sup>6<\/sup> \u2212 2x<sup>4<\/sup> + 9x<sup>3<\/sup> + 2x \u2212 4) \u2212 (7x<sup>5<\/sup> \u2212 8x<sup>4<\/sup> + 2x\u2212 11)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 11\" width=\"535\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-11.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-11-300x57.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 12.<br \/>\n(4x<sup>5<\/sup> \u2212 7x<sup>3<\/sup> \u2212 9x<sup>2<\/sup> + 18) \u2212 (14x<sup>5<\/sup> \u2212 8x<sup>4<\/sup> + 11x<sup>2<\/sup> + x)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n(8x<sup>5<\/sup> + 6x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> + 10x) \u2212 (9x<sup>5<\/sup> \u2212 x<sup>3<\/sup> \u2212 13x<sup>2<\/sup> + 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 13\" width=\"502\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-13.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-13-300x57.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Question 14.<br \/>\n(11x<sup>4<\/sup> \u2212 9x<sup>2<\/sup> + 3x + 11) \u2212 (2x<sup>4<\/sup> + 6x<sup>3<\/sup> + 2x \u2212 9)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> During a recent period of time, the numbers (in thousands) of males Mand females F that attend degree-granting institutions in the United States can be modeled by<br \/>\nM = 19.7t<sup>2<\/sup> + 310.5t + 7539.6<br \/>\nF = 28t<sup>2<\/sup> + 368t + 10127.8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 19\" width=\"172\" height=\"254\" \/><br \/>\nwhere t is time in years. Write a polynomial to model the total number of people attending degree-granting institutions. Interpret its constant term.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 15\" width=\"519\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-15.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-15-300x128.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 16.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> A farmer plants a garden that contains corn and pumpkins. The total area (in square feet) of the garden is modeled by the expression 2x<sup>2<\/sup> + 5x + 4. The area of the corn is modeled by the expression x<sup>2<\/sup> \u2212 3x + 2. Write an expression that models the area of the pumpkins.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 17\u201324, find the product.<\/b><\/p>\n<p>Question 17.<br \/>\n7x<sup>3<\/sup>(5x<sup>2<\/sup> + 3x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 17\" width=\"368\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-17.png 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-17-300x29.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/p>\n<p>Question 18.<br \/>\n\u22124x<sup>5<\/sup>(11x<sup>3<\/sup> + 2x<sup>2<\/sup> + 9x + 1)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n(5x<sup>2<\/sup> \u2212 4x + 6)(\u22122x + 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 19\" width=\"459\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-19.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-19-300x88.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 20.<br \/>\n(\u2212x \u2212 3)(2x<sup>2<\/sup> + 5x + 8)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n(x<sup>2<\/sup> \u2212 2x \u2212 4)(x<sup>2<\/sup> \u2212 3x \u2212 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 21\" width=\"558\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-21.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-21-300x73.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 22.<br \/>\n(3x<sup>2<\/sup> + x \u2212 2)(\u22124x<sup>2<\/sup> \u2212 2x \u2212 1)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n(3x<sup>3<\/sup> \u2212 9x + 7)(x<sup>2<\/sup> \u2212 2x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 23\" width=\"554\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-23.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-23-300x73.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 24.<br \/>\n(4x<sup>2<\/sup> \u2212 8x \u2212 2)(x<sup>4<\/sup> + 3x<sup>2<\/sup> + 4x)<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 25 and 26, describe and correct the error in performing the operation.<\/b><\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-20.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 20\" width=\"378\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-20.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-20-300x102.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 25\" width=\"572\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-25.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-25-300x68.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 21\" width=\"382\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-21.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-21-300x104.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 27\u201332, find the product of the binomials.<\/b><\/p>\n<p>Question 27.<br \/>\n(x \u2212 3)(x + 2)(x + 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47607\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 27\" width=\"522\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-27.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-27-300x79.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 28.<br \/>\n(x \u2212 5)(x + 2)(x \u2212 6)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n(x \u2212 2)(3x + 1)(4x \u2212 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 29\" width=\"407\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-29.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-29-300x125.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><\/p>\n<p>Question 30.<br \/>\n(2x + 5)(x \u2212 2)(3x + 4)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n(3x \u2212 4)(5 \u2212 2x)(4x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 31\" width=\"503\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-31.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-31-300x101.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 32.<br \/>\n(4 \u2212 5x)(1 \u2212 2x)(3x + 2)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<b>REASONING<\/b> Prove the polynomial identity (a + b)(a \u2212 b) = a<sup>2<\/sup> \u2212 b<sup>2<\/sup>. Then give an example of two whole numbers greater than 10 that can be multiplied using mental math and the given identity. Justify your answers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 33\" width=\"579\" height=\"485\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-33.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-33-300x251.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>NUMBER SENSE<\/b> You have been asked to order textbooks for your class. You need to order 29 textbooks that cost $31 each. Explain how you can use the polynomial identity (a + b)(a \u2212 b) = a<sup>2<\/sup> \u2212 b<sup>2<\/sup> and mental math to find the total cost of the textbooks.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-22.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 22\" width=\"262\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-22.png 262w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-22-150x150.png 150w\" sizes=\"(max-width: 262px) 100vw, 262px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 35\u201342, find the product.<\/b><\/p>\n<p>Question 35.<br \/>\n(x \u2212 9)(x + 9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 35\" width=\"245\" height=\"62\" \/><\/p>\n<p>Question 36.<br \/>\n(m + 6)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n(3c \u2212 5)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 37\" width=\"324\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-37.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-37-300x59.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>Question 38.<br \/>\n(2y \u2212 5)(2y + 5)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n(7h + 4)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47613\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 39\" width=\"333\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-39.png 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-39-300x58.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p>Question 40.<br \/>\n(9g \u2212 4)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n(2k + 6)<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 41\" width=\"463\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-41.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-41-300x40.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 42.<br \/>\n(4n \u2212 3)<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 43\u201348, use Pascal\u2019s Triangle to expand the binomial.<\/b><\/p>\n<p>Question 43.<br \/>\n(2t + 4)<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47615\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 43\" width=\"573\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-43.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-43-300x65.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 44.<br \/>\n(6m + 2)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n(2q \u2212 3)<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47616\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 45\" width=\"563\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-45.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-45-300x88.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 46.<br \/>\n(g + 2)<sup>5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n(yz + 1)<sup>5<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47617\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 47\" width=\"575\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-47.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-47-300x86.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 48.<br \/>\n(np \u2212 1)<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>COMPARING METHODS<\/b> Find the product of the expression (a<sup>2<\/sup> + 4b<sup>2<\/sup>)<sup>2<\/sup>(3a<sup>2<\/sup> \u2212 b<sup>2<\/sup>)<sup>2<\/sup> using two different methods. Which method do you prefer? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47618\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 49\" width=\"545\" height=\"632\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-49.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-49-259x300.png 259w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>THOUGHT PROVOKING<\/b> Adjoin one or more polygons to the rectangle to form a single new polygon whose perimeter is double that of the rectangle. Find the perimeter of the new polygon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 23\" width=\"235\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p><b>MATHEMATICAL CONNECTIONS In Exercises 51 and 52, write an expression for the volume of the figure as a polynomial in standard form.<\/b><\/p>\n<p>Question 51.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-24.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 24\" width=\"147\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47619\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 51\" width=\"386\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-51.png 386w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-51-300x160.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 25\" width=\"161\" height=\"122\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>Two people make three deposits into their bank accounts earning the same simple interest rate r.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-26.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 26\" width=\"282\" height=\"264\" \/><br \/>\nPerson A\u2019s account is worth 2000(1 + r)<sup>3<\/sup> + 3000(1 + r)<sup>2<\/sup> + 1000(1 + r) on January 1, 2015.<br \/>\na. Write a polynomial for the value of Person B\u2019s account on January 1, 2015.<br \/>\nb. Write the total value of the two accounts as a polynomial in standard form. Then interpret the coefficients of the polynomial.<br \/>\nc. Suppose their interest rate is 0.05. What is the total value of the two accounts on January 1, 2015?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47620\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-53.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 53.1\" width=\"579\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-53.1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-53.1-300x238.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-53.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 53.2\" width=\"414\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-53.2.png 414w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-53.2-300x151.png 300w\" sizes=\"(max-width: 414px) 100vw, 414px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>PROBLEM SOLVING<\/b><br \/>\nThe sphere is centered in the cube. Find an expression for the volume of the cube outside the sphere.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 27\" width=\"194\" height=\"161\" \/><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend claims the sum of two binomials is always a binomial and the product of two binomials is always a trinomial. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 55\" width=\"556\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-55.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-55-300x47.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> You make a tin box by cutting x-inch-by-x-inch pieces of tin off the corners of a rectangle and folding up each side. The plan for your box is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-28.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 28\" width=\"315\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-28.png 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-28-300x156.png 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\na. What are the dimensions of the original piece of tin?<br \/>\nb. Write a function that represents the volume of the box. Without multiplying, determine its degree.<br \/>\nAnswer:<\/p>\n<p><b>USING TOOLS In Exercises 57\u201360, use a graphing calculator to make a conjecture about whether the two functions are equivalent. Explain your reasoning.<\/b><\/p>\n<p>Question 57.<br \/>\nf(x) = (2x \u2212 3)<sup>3<\/sup>; g(x) = 8x<sup>3<\/sup> \u2212 36x<sup>2<\/sup> + 54x \u2212 27<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 57\" width=\"556\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-57.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-57-300x120.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 58.<br \/>\nh(x) = (x + 2)<sup>5<\/sup>;<br \/>\nk(x) = x<sup>5<\/sup> + 10x<sup>4<\/sup> + 40x<sup>3<\/sup> + 80x<sup>2<\/sup> + 64x<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\nf(x) = (\u2212x \u2212 3)<sup>4<\/sup>;<br \/>\ng(x) = x<sup>4<\/sup> + 12x<sup>3<\/sup> + 54x<sup>2<\/sup> + 108x + 80<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 59\" width=\"545\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-59.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-59-300x119.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 60.<br \/>\nf(x) = (\u2212x + 5)<sup>3<\/sup>; g(x) = \u2212x<sup>3<\/sup> + 15x<sup>2<\/sup> \u2212 75x + 125<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<b>REASONING<\/b> Copy Pascal\u2019s Triangle and add rows for n = 6, 7, 8, 9, and 10. Use the new rows to expand (x + 3)<sup>7<\/sup> and (x \u2212 5)<sup>9<\/sup>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-61.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 61.1\" width=\"557\" height=\"525\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-61.1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-61.1-300x283.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-61.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 61.2\" width=\"592\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-61.2.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-61.2-300x114.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 62.<br \/>\n<b>ABSTRACT REASONING<\/b> You are given the function f(x) = (x + a)(x + b)(x + c)(x + d). When f(x) is written in standard form, show that the coefficient of x<sup>3<\/sup> is the sum of a, b, c, and d, and the constant term is the product of a, b, c, and d.<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>DRAWING CONCLUSIONS<\/b> Let g(x) = 12x<sup>4<\/sup> + 8x + 9 and h(x) = 3x<sup>5<\/sup> + 2x<sup>3<\/sup> \u2212 7x + 4.<br \/>\na. What is the degree of the polynomial g(x) + h(x)?<br \/>\nb. What is the degree of the polynomial g(x) \u2212 h(x)?<br \/>\nc. What is the degree of the polynomial g(x) \u2022 h(x)?<br \/>\nd. In general, if g(x) and h(x) are polynomials such that g(x) has degree m and h(x) has degree n, and m &gt; n, what are the degrees of g(x) + h(x), g(x) \u2212 h(x), and g(x) \u2022 h(x)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-63.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 63.1\" width=\"598\" height=\"503\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-63.1.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-63.1-300x252.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 64.<br \/>\n<b>FINDING A PATTERN<\/b> In this exercise, you will explore the sequence of square numbers. The first four square numbers are represented below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 29\" width=\"296\" height=\"82\" \/><br \/>\na. Find the differences between consecutive square numbers. Explain what you notice.<br \/>\nb. Show how the polynomial identity (n + 1)<sup>2<\/sup> \u2212 n<sup>2<\/sup> = 2n + 1 models the differences between square numbers.<br \/>\nc. Prove the polynomial identity in part (b).<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<b>CRITICAL THINKING<\/b> Recall that a Pythagorean triple is a set of positive integers a, b, and c such that a<sup>2<\/sup> + b<sup>2<\/sup> = c<sup>2<\/sup>. The numbers 3, 4, and 5 form a Pythagorean triple because 3<sup>2<\/sup> + 4<sup>2<\/sup> = 5<sup>2<\/sup>. You can use the polynomial identity (x<sup>2<\/sup> \u2212 y<sup>2<\/sup>)<sup>2<\/sup> + (2xy)<sup>2<\/sup> = (x<sup>2<\/sup> + y<sup>2<\/sup>)<sup>2<\/sup> to generate other Pythagorean triples.<br \/>\na. Prove the polynomial identity is true by showing that the simplified expressions for the left and right sides are the same. b. Use the identity to generate the Pythagorean triple when x = 6 and y = 5.<br \/>\nc. Verify that your answer in part (b) satisfies a<sup>2<\/sup> + b<sup>2<\/sup> = c<sup>2<\/sup>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-65.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 65.1\" width=\"574\" height=\"414\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-65.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-65.1-300x216.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-65.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 65.2\" width=\"426\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-65.2.png 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-65.2-300x162.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Perform the operation. Write the answer in standard form. <\/b>(Section 3.2)<\/p>\n<p>Question 66.<br \/>\n(3 \u2212 2i) + (5 + 9i)<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n(12 + 3i) \u2212 (7 \u2212 8i)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-67.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 67\" width=\"415\" height=\"64\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-67.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-67-300x46.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p>Question 68.<br \/>\n(7i)(\u22123i)<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n(4 + i)(2 \u2212 i)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-69.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.2 Question 69\" width=\"321\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-69.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.2-Question-69-300x94.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<h3><a id=\"Lesson_4.3_Dividing_Polynomials\"><\/a>Lesson 4.3 Dividing Polynomials<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you use the factors of a cubic polynomial to solve a division problem involving the polynomial?<\/p>\n<p><b>EXPLORATION 1<br \/>\nDividing Polynomials<br \/>\nWork with a partner. <\/b>Match each division statement with the graph of the related cubic polynomial f(x). Explain your reasoning. Use a graphing calculator to verify your answers.<br \/>\na. \\(\\frac{f(x)}{x}\\) = (x \u2212 1)(x + 2)<br \/>\nb. \\(\\frac{f(x)}{x-1}\\) = (x \u2212 1)(x + 2)<br \/>\nc. \\(\\frac{f(x)}{x+1}\\) = (x \u2212 1)(x + 2)<br \/>\nd. \\(\\frac{f(x)}{x-2}\\) = (x\u2212 1)(x+ 2)<br \/>\ne. \\(\\frac{f(x)}{x+2}\\) = (x\u2212 1)(x+ 2)<br \/>\nf. \\(\\frac{f(x)}{x-3}\\) = (x\u2212 1)(x+ 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-29.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 29.1\" width=\"562\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-29.1.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-29.1-300x239.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nDividing Polynomials<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-30.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 30\" width=\"262\" height=\"172\" \/><br \/>\n<b>Work with a partner. <\/b>Use the results of Exploration 1 to find each quotient. Write your answers in standard form. Check your answers by multiplying.<br \/>\na. (x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 2x) \u00f7 x<br \/>\nb. (x<sup>3<\/sup> \u2212 3x + 2) \u00f7 (x \u2212 1)<br \/>\nc. (x<sup>3<\/sup> + 2x<sup>2<\/sup> \u2212 x \u2212 2) \u00f7 (x + 1)<br \/>\nd. (x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 4x + 4) \u00f7 (x \u2212 2)<br \/>\ne. (x<sup>3<\/sup> + 3x<sup>2<\/sup> \u2212 4) \u00f7 (x + 2)<br \/>\nf. (x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 5x + 6) \u00f7 (x \u2212 3)<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you use the factors of a cubic polynomial to solve a division problem involving the polynomial?<\/p>\n<p><b>4.3 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Divide using polynomial long division.<\/b><\/p>\n<p>Question 1.<br \/>\n(x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 2x + 8) \u00f7 (x \u2212 1)<\/p>\n<p>Question 2.<br \/>\n(x<sup>4<\/sup> + 2x<sup>2<\/sup> \u2212 x + 5) \u00f7 (x<sup>2<\/sup> \u2212 x + 1)<\/p>\n<p><b>Divide using synthetic division.<\/b><\/p>\n<p>Question 3.<br \/>\n(x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> \u2212 7x + 6) \u00f7 (x \u2212 2)<\/p>\n<p>Question 4.<br \/>\n(2x<sup>3<\/sup> \u2212 x \u2212 7) \u00f7 (x + 3)<\/p>\n<p><b>Use synthetic division to evaluate the function for the indicated value of x.<\/b><\/p>\n<p>Question 5.<br \/>\nf(x) = 4x<sup>2<\/sup> \u2212 10x \u2212 21; x = 5<\/p>\n<p>Question 6.<br \/>\nf(x) = 5x<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 20x \u2212 6; x = 2<\/p>\n<h3><a id=\"Dividing_Polynomials_4.3_Exercises\"><\/a>Dividing Polynomials 4.3 Exercises<\/h3>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p>Question 1.<br \/>\n<b>WRITING<\/b> Explain the Remainder Theorem in your own words. Use an example in your explanation.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 1\" width=\"535\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-1.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-1-300x108.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY<\/b> What form must the divisor have to make synthetic division an appropriate method for dividing a polynomial? Provide examples to support your claim.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<b>VOCABULARY<\/b> Write the polynomial divisor, dividend, and quotient functions represented by the synthetic division shown at the right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 31\" width=\"203\" height=\"90\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 3\" width=\"441\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-3.png 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-3-300x25.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>WRITING<\/b> Explain what the colored numbers represent in the synthetic division in Exercise 3.<br \/>\nAnswer:<\/p>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p><b>In Exercises 5\u201310, divide using polynomial long division.<\/b><\/p>\n<p>Question 5.<br \/>\n(x<sup>2<\/sup> + x \u2212 17 ) \u00f7 (x \u2212 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47635\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 5\" width=\"406\" height=\"224\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-5.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-5-300x166.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 6.<br \/>\n(3x<sup>2<\/sup> \u2212 14x \u2212 5) \u00f7 (x \u2212 5)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n(x<sup>3<\/sup> + x<sup>2<\/sup> + x + 2 ) \u00f7 (x<sup>2<\/sup> \u2212 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47636\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 7\" width=\"451\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-7.png 451w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-7-300x150.png 300w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p>Question 8.<br \/>\n(7x<sup>3<\/sup> + x<sup>2<\/sup> + x ) \u00f7 (x<sup>2<\/sup> + 1)<\/p>\n<p>Answer:<\/p>\n<p>Question 9.<br \/>\n(5x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> \u2212 7x<sup>2<\/sup> \u2212 39) \u00f7 (x<sup>2<\/sup> + 2x \u2212 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47637\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 9\" width=\"442\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-9.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-9-300x230.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>Question 10.<br \/>\n(4x<sup>4<\/sup> + 5x \u2212 4) \u00f7 (x<sup>2<\/sup> \u2212 3x \u2212 2)<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 11\u201318, divide using synthetic division.<\/b><\/p>\n<p>Question 11.<br \/>\n(x<sup>2<\/sup> + 8x + 1) \u00f7 (x \u2212 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47638\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 11\" width=\"539\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-11.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-11-300x114.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 12.<br \/>\n(4x<sup>2<\/sup> \u2212 13x \u2212 5) \u00f7 (x \u2212 2)<br \/>\nAnswer:<\/p>\n<p>(4x<sup>2<\/sup> \u2212 13x \u2212 5) \u00f7 (x \u2212 2)<\/p>\n<p>use synthetic division. Because the divisor is x-2 , k=2<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Question 13.<br \/>\n(2x<sup>2<\/sup> \u2212 x + 7) \u00f7 (x + 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47639\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 13\" width=\"425\" height=\"228\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-13.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-13-300x161.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>Question 14.<br \/>\n(x<sup>3<\/sup> \u2212 4x + 6) \u00f7 (x + 3)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n(x<sup>2<\/sup> + 9) \u00f7 (x \u2212 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47640\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 15\" width=\"541\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-15.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-15-300x109.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 16.<br \/>\n(3x<sup>3<\/sup> \u2212 5x<sup>2<\/sup> \u2212 2) \u00f7 (x \u2212 1)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n(x<sup>4<\/sup> \u2212 5x<sup>3<\/sup> \u2212 8x<sup>2<\/sup> + 13x \u2212 12) \u00f7 (x \u2212 6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47641\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 17\" width=\"545\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-17.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-17-300x111.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 18.<br \/>\n(x<sup>4<\/sup> + 4x<sup>3<\/sup> + 16x \u2212 35) \u00f7 (x + 5 )<br \/>\nAnswer:<\/p>\n<p><b>ANALYZING RELATIONSHIPS In Exercises 19\u201322, match the equivalent expressions. Justify your answers.<\/b><\/p>\n<p>Question 19.<br \/>\n(x<sup>2<\/sup> + x \u2212 3) \u00f7 (x \u2212 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47642\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 19\" width=\"463\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-19.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-19-300x20.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><\/p>\n<p>Question 20.<br \/>\n(x<sup>2<\/sup> \u2212 x \u2212 3) \u00f7 (x \u2212 2)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n(x<sup>2<\/sup> \u2212 x + 3) \u00f7 (x \u2212 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47643\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 21\" width=\"467\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-21.png 467w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-21-300x22.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>Question 22.<br \/>\n(x<sup>2<\/sup> + x + 3) \u00f7 (x \u2212 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-32.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 32\" width=\"337\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-32.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-32-300x93.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 23 and 24, describe and correct the error in using synthetic division to divide x<sup>3<\/sup> &#8211; 5x + 3 by x &#8211; 2.<\/b><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 33\" width=\"366\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-33.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-33-300x136.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47644\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 23\" width=\"540\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-23.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-23-300x112.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-34.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 34\" width=\"365\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-34.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-34-300x135.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 25\u201332, use synthetic division to evaluate the function for the indicated value of x.<\/b><\/p>\n<p>Question 25.<br \/>\nf(x) = \u2212x<sup>2<\/sup> \u2212 8x + 30; x = \u22121<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47645\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 25\" width=\"473\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-25.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-25-300x106.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = 3x<sup>2<\/sup> + 2x \u2212 20; x = 3<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> + 4x + 3; x = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 27\" width=\"476\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-27.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-27-300x101.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 28.<br \/>\nf(x) = x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 3x + 9; x = \u22124<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 6x + 1; x = 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47647\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 29\" width=\"495\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-29.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-29-300x97.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 30.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 9x \u2212 7; x = 10<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nf(x) = x<sup>4<\/sup> + 6x<sup>2<\/sup> \u2212 7x + 1; x = 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47648\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 31\" width=\"491\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-31.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-31-300x98.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 32.<br \/>\nf(x) = \u2212x<sup>4<\/sup> \u2212 x<sup>3<\/sup> \u2212 2; x = 5<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<b>MAKING AN ARGUMENT<\/b> You use synthetic division to divide f(x) by (x \u2212 a) and find that the remainder equals 15. Your friend concludes that f(15) = a. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47649\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 33\" width=\"485\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-33.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-33-300x35.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/p>\n<p>Question 34.<br \/>\n<b>THOUGHT PROVOKING<\/b> A polygon has an area represented by A = 4x<sup>2<\/sup> + 8x + 4. The figure has at least one dimension equal to 2x + 2. Draw the figure and label its dimensions.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<b>USING TOOLS<\/b> The total attendance A (in thousands) at NCAA women\u2019s basketball games and the number T of NCAA women\u2019s basketball teams over a period of time can be modeled by<br \/>\nA = \u22121.95x<sup>3<\/sup> + 70.1x<sup>2<\/sup> \u2212 188x + 2150<br \/>\nT = 14.8x + 725<br \/>\nwhere x is in years and 0 &lt; x &lt; 18. Write a function for the average attendance per team over this period of time.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 35\" width=\"235\" height=\"194\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47650\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 35\" width=\"483\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-35.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-35-300x55.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><\/p>\n<p>Question 36.<br \/>\n<b>COMPARING METHODS<\/b> The profit P (in millions of dollars) for a DVD manufacturer can be modeled by P = \u22126x<sup>3<\/sup> + 72x, where x is the number (in millions) of DVDs produced. Use synthetic division to show that the company yields a profit of $96 million when 2 million DVDs are produced. Is there an easier method? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<b>CRITICAL THINKING<\/b> What is the value of k such that (x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + kx \u2212 30) \u00f7 (x \u2212 5) has a remainder of zero?<br \/>\nA. \u221214<br \/>\nB. \u22122<br \/>\nC. 26<br \/>\nD. 32<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47651\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 37\" width=\"306\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-37.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-37-300x124.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/p>\n<p>Question 38.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>The graph represents the polynomial function f(x) = x<sup>3<\/sup> + 3x<sup>2<\/sup> \u2212 x \u2212 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-36.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 36\" width=\"227\" height=\"178\" \/><br \/>\na. The expression f(x) \u00f7 (x \u2212 k) has a remainder of \u221215. What is the value of k?<br \/>\nb. Use the graph to compare the remainders of (x<sup>3<\/sup> + 3x<sup>2<\/sup> \u2212 x \u2212 3) \u00f7 (x + 3) and (x<sup>3<\/sup> + 3x<sup>2<\/sup> \u2212 x \u2212 3) \u00f7 (x + 1).<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> The volume V of the rectangular prism is given by V = 2x<sup>3<\/sup> + 17x<sup>2<\/sup> + 46x + 40. Find an expression for the missing dimension.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 37\" width=\"229\" height=\"121\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 39\" width=\"562\" height=\"311\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-39.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-39-300x166.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 40.<br \/>\n<b>USING STRUCTURE<\/b> You divide two polynomials and obtain the result 5x<sup>2<\/sup> \u2212 13x + 47 \u2212 \\(\\frac{102}{x+2}\\). What is the dividend? How did you find it?<br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Find the zero(s) of the function. <\/b>(Sections 3.1and 3.2)<\/p>\n<p>Question 41.<br \/>\nf(x) = x<sup>2<\/sup> \u2212 6x + 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 41\" width=\"184\" height=\"167\" \/><\/p>\n<p>Question 42.<br \/>\ng(x) = 3(x + 6)(x \u2212 2)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ng(x) = x<sup>2<\/sup> + 14x + 49<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.3-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.3 Question 43\" width=\"220\" height=\"166\" \/><\/p>\n<p>Question 44.<br \/>\nh(x) = 4x<sup>2<\/sup> + 36<\/p>\n<h3><a id=\"Lesson_4.4_Factoring_Polynomials\"><\/a>Lesson 4.4 Factoring Polynomials<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you factor a polynomial?<\/p>\n<p><b>EXPLORATION 1<br \/>\nFactoring Polynomials<br \/>\nWork with a partner.<\/b> Match each polynomial equation with the graph of its related polynomial function. Use the x-intercepts of the graph to write each polynomial in factored form. Explain your reasoning.<br \/>\na. x<sup>2<\/sup> + 5x + 4 = 0<br \/>\nb. x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 x + 2 = 0<br \/>\nc. x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 2x = 0<br \/>\nd. x<sup>3<\/sup> \u2212 x = 0<br \/>\ne. x<sup>4<\/sup> \u2212 5x<sup>2<\/sup> + 4 = 0<br \/>\nf. x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + 2x = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-38.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 38\" width=\"535\" height=\"460\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-38.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-38-300x258.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nFactoring Polynomials<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 39\" width=\"260\" height=\"197\" \/><br \/>\n<b>Work with a partner.<\/b> Use the x-intercepts of the graph of the polynomial function to write each polynomial in factored form. Explain your reasoning. Check your answers by multiplying.<br \/>\na. f(x) = x<sup>2<\/sup> \u2212 x \u2212 2<br \/>\nb. f(x) = x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 2x<br \/>\nc. f(x) = x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 3x<br \/>\nd. f(x) = x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> \u2212 x + 3<br \/>\ne. f(x) = x<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 2x<br \/>\nf. f(x) = x<sup>4<\/sup> \u2212 10x<sup>2<\/sup> + 9<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you factor a polynomial?<\/p>\n<p>Question 4.<br \/>\nWhat information can you obtain about the graph of a polynomial function written in factored form?<\/p>\n<p><b>4.4 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nx<sup>3<\/sup> \u2212 7x<sup>2<\/sup> + 10x<\/p>\n<p>Question 2.<br \/>\n3n<sup>7<\/sup> \u2212 75n<sup>5<\/sup><\/p>\n<p>Question 3.<br \/>\n8m<sup>5<\/sup> \u2212 16m<sup>4<\/sup> + 8m<sup>3<\/sup><\/p>\n<p><b>Factor the polynomial completely<\/b><\/p>\n<p>Question 4.<br \/>\na<sup>3<\/sup> + 27<\/p>\n<p>Question 5.<br \/>\n6z<sup>5<\/sup> \u2212 750z<sup>2<\/sup><\/p>\n<p>Question 6.<br \/>\nx<sup>3<\/sup> + 4x<sup>2<\/sup> \u2212 x \u2212 4<\/p>\n<p>Question 7.<br \/>\n3y<sup>3<\/sup> + y<sup>2<\/sup> + 9y + 3<\/p>\n<p>Question 8.<br \/>\n\u221216n<sup>4<\/sup> + 625<\/p>\n<p>Question 9.<br \/>\n5w<sup>6<\/sup> \u2212 25w<sup>4<\/sup> + 30w<sup>2<\/sup><\/p>\n<p>Question 10.<br \/>\nDetermine whether x\u2212 4 is a factor of f(x) = 2x<sup>2<\/sup> + 5x \u2212 12.<\/p>\n<p>Question 11.<br \/>\nShow that x \u2212 6 is a factor of f(x) = x<sup>3<\/sup> \u2212 5x<sup>2<\/sup> \u2212 6x. Then factor f(x) completely.<\/p>\n<p>Question 12.<br \/>\nIn Example 7, does your answer change when you first determine whether 2 is a zero and then whether \u22121 is a zero? Justify your answer.<\/p>\n<h3><a id=\"Factoring_Polynomials_4.4_Exercises\"><\/a>Factoring Polynomials 4.4 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE <\/b>The expression 9x<sup>4<\/sup> \u2212 49 is in _________ form because it can be written as u<sup>2<\/sup> \u2212 49 where u = _____.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 1\" width=\"579\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-1-300x31.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY <\/b>Explain when you should try factoring a polynomial by grouping.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<b>WRITING <\/b>How do you know when a polynomial is factored completely?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 3\" width=\"541\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-3.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-3-300x33.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 4.<br \/>\n<b>WRITING <\/b>Explain the Factor Theorem and why it is useful.<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 5\u201312, factor the polynomial completely.<\/b><\/p>\n<p>Question 5.<br \/>\nx<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 24x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47657\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 5\" width=\"334\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-5.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-5-300x58.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 6.<br \/>\n4k<sup>5<\/sup> \u2212 100k<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n3p<sup>5<\/sup> \u2212 192p<sup>3<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 7\" width=\"324\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-7.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-7-300x62.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>Question 8.<br \/>\n2m<sup>6<\/sup> \u2212 24m<sup>5<\/sup> + 64m<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n2q<sup>4<\/sup> + 9q<sup>3<\/sup> \u2212 18q<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47659\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 9\" width=\"375\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-9.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-9-300x52.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\n<p>Question 10.<br \/>\n3r<sup>6<\/sup> \u2212 11r<sup>5<\/sup> \u2212 20r<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n10w<sup>10<\/sup> \u2212 19w<sup>9<\/sup> + 6w<sup>8<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47660\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 11\" width=\"422\" height=\"69\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-11.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-11-300x49.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 12.<br \/>\n18v<sup>9<\/sup> + 33v<sup>8<\/sup> + 14v<sup>7<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201320, factor the polynomial completely.<\/b><\/p>\n<p>Question 13.<br \/>\nx<sup>3<\/sup> + 64<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47661\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 13\" width=\"318\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-13.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-13-300x63.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p>Question 14.<br \/>\ny<sup>3<\/sup> + 512<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ng<sup>3<\/sup> \u2212 343<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47662\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 15\" width=\"336\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-15.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-15-300x59.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p>Question 16.<br \/>\nc<sup>3<\/sup> \u2212 27<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n3h<sup>9<\/sup> \u2212 192h<sup>6<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47663\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 17\" width=\"395\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-17.png 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-17-300x78.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Question 18.<br \/>\n9n<sup>6<\/sup> \u2212 6561n<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n16t<sup>7<\/sup> + 250t<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47664\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 19\" width=\"405\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-19.png 405w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-19-300x76.png 300w\" sizes=\"(max-width: 405px) 100vw, 405px\" \/><\/p>\n<p>Question 20.<br \/>\n135z<sup>11<\/sup> \u2212 1080z<sup>8<\/sup><br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 21 and 22, describe and correct the error in factoring the polynomial.<\/b><\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-40.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 40\" width=\"372\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-40.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-40-300x96.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47665\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 21\" width=\"567\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-21.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-21-300x47.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 41\" width=\"366\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-41.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-41-300x107.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 23\u201330, factor the polynomial completely.<\/b><\/p>\n<p>Question 23.<br \/>\ny<sup>3<\/sup> \u2212 5y<sup>2<\/sup> + 6y \u2212 30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47666\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 23\" width=\"421\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-23.png 421w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-23-300x48.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p>Question 24.<br \/>\nm<sup>3<\/sup> \u2212 m<sup>2<\/sup> + 7m \u2212 72<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n3a<sup>3<\/sup> + 18a<sup>2<\/sup> + 8a + 48<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47667\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 25\" width=\"458\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-25.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-25-300x45.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>Question 26.<br \/>\n2k<sup>3<\/sup> \u2212 20k<sup>2<\/sup> + 5k \u2212 50<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nx<sup>3<\/sup> \u2212 8x<sup>2<\/sup> \u2212 4x + 32<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47668\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 27\" width=\"428\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-27.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-27-300x73.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Question 28.<br \/>\nz<sup>3<\/sup> \u2212 5z<sup>2<\/sup> \u2212 9z + 45<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n4q<sup>3<\/sup> \u2212 16q<sup>7<\/sup> \u2212 9q + 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47669\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 29\" width=\"477\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-29.png 477w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-29-300x65.png 300w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/p>\n<p>Question 30.<br \/>\n16n<sup>3<\/sup> + 32n<sup>7<\/sup> \u2212 n \u2212 2<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 31\u201338, factor the polynomial completely.<\/b><\/p>\n<p>Question 31.<br \/>\n49k<sup>4<\/sup> \u2212 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47670\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 31\" width=\"290\" height=\"68\" \/><\/p>\n<p>Question 32.<br \/>\n4m<sup>4<\/sup> \u2212 25<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nc<sup>4<\/sup> + 9c<sup>2<\/sup> + 20<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47671\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 33\" width=\"319\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-33.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-33-300x33.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Question 34.<br \/>\ny<sup>4<\/sup> \u2212 3y<sup>2<\/sup> \u2212 28<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n16z<sup>4<\/sup> \u2212 81<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47672\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 35\" width=\"372\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-35.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-35-300x80.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/p>\n<p>Question 36.<br \/>\n81a<sup>4<\/sup> \u2212 256<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n3r<sup>8<\/sup> + 3r<sup>5<\/sup> \u2212 60r<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47673\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 37\" width=\"372\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-37.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-37-300x55.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/p>\n<p>Question 38.<br \/>\n4n<sup>12<\/sup> \u2212 32n<sup>7<\/sup> + 48n<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 39\u201344, determine whether the binomial is a factor of the polynomial.<\/b><\/p>\n<p>Question 39.<br \/>\nf(x) = 2x<sup>3<\/sup> + 5x<sup>2<\/sup> \u2212 37x \u2212 60; x \u2212 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47674\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 39\" width=\"476\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-39.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-39-300x127.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 40.<br \/>\ng(x) = 3x<sup>3<\/sup> \u2212 28x<sup>2<\/sup> + 29x + 140; x + 7<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nh(x) = 6x<sup>5<\/sup> \u2212 15x<sup>4<\/sup> \u2212 9x<sup>3<\/sup>; x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 41\" width=\"533\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-41.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-41-300x110.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 42.<br \/>\ng(x) = 8x<sup>5<\/sup> \u2212 58x<sup>4<\/sup> + 60x<sup>3<\/sup> + 140; x \u2212 6<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nh(x) = 6x<sup>4<\/sup> \u2212 6x<sup>3<\/sup> \u2212 84x<sup>2<\/sup> + 144x; x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47676\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 43\" width=\"502\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-43.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-43-300x117.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p>Question 44.<br \/>\nt(x) = 48x<sup>4<\/sup> + 36x<sup>3<\/sup> \u2212 138x<sup>2<\/sup> \u2212 36x; x + 2<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 45\u201350, show that the binomial is a factor of the polynomial. Then factor the polynomial completely.<\/b><\/p>\n<p>Question 45.<br \/>\ng(x) = x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 20x; x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47677\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 45\" width=\"588\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-45.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-45-300x168.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 46.<br \/>\nt(x) = x<sup>3<\/sup> \u2212 5x<sup>2<\/sup> \u2212 9x + 45; x \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 6x<sup>3<\/sup> \u2212 8x + 48; x \u2212 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47678\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 47\" width=\"558\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-47.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-47-300x180.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 48.<br \/>\ns(x) = x<sup>4<\/sup> + 4x<sup>3<\/sup> \u2212 64x \u2212 256; x + 4<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nr(x) = x<sup>3<\/sup> \u2212 37x + 84; x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47679\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 49\" width=\"584\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-49.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-49-300x171.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 50.<br \/>\nh(x) = x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 24x \u2212 36; x + 2<br \/>\nAnswer:<\/p>\n<p><b>ANALYZING RELATIONSHIPS In Exercises 51\u201354, match the function with the correct graph. Explain your reasoning.<\/b><\/p>\n<p>Question 51.<br \/>\nf(x) = (x \u2212 2)(x \u2212 3)(x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47680\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 51\" width=\"454\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-51.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-51-300x21.png 300w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><\/p>\n<p>Question 52.<br \/>\ng(x) = x(x + 2)(x + 1)(x \u2212 2)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\nh(x) = (x + 2)(x + 3)(x \u2212 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47681\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 53\" width=\"476\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-53.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-53-300x20.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 54.<br \/>\nk(x) = x(x \u2212 2)(x \u2212 1)(x + 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-42.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 42\" width=\"389\" height=\"304\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-42.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-42-300x234.png 300w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The volume (in cubic inches) of a shipping box is modeled by V = 2x<sup>3<\/sup> \u2212 19x<sup>2<\/sup> + 39x, where x is the length (in inches). Determine the values of x for which the model makes sense. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 43\" width=\"225\" height=\"187\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47682\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 55\" width=\"596\" height=\"535\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-55.png 596w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-55-300x269.png 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The volume (in cubic inches) of a rectangular birdcage can be modeled by V = 3x<sup>3<\/sup> \u2212 17x<sup>2<\/sup> + 29x \u2212 15, where x is the length (in inches). Determine the values of x for which the model makes sense. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-44.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 44\" width=\"173\" height=\"178\" \/><br \/>\nAnswer:<\/p>\n<p><b>USING STRUCTURE In Exercises 57\u201364, use the method of your choice to factor the polynomial completely. Explain your reasoning.<\/b><\/p>\n<p>Question 57.<br \/>\na<sup>6<\/sup> + a<sup>5<\/sup> \u2212 30a<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47683\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 57\" width=\"492\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-57.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-57-300x79.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><\/p>\n<p>Question 58.<br \/>\n8m<sup>3<\/sup> \u2212 343<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\nz<sup>3<\/sup> \u2212 7z<sup>2<\/sup> \u2212 9z + 63<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47684\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 59\" width=\"543\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-59.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-59-300x122.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 60.<br \/>\n2p<sup>8<\/sup> \u2212 12p<sup>5<\/sup> + 16p<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n64r<sup>3<\/sup> + 729<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47685\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-61.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 61\" width=\"504\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-61.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-61-300x77.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Question 62.<br \/>\n5x<sup>5<\/sup> \u2212 10x<sup>4<\/sup> \u2212 40x<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n16n<sup>4<\/sup> \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47686\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-63.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 63\" width=\"577\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-63.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-63-300x85.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 64.<br \/>\n9k<sup>3<\/sup> \u2212 24k<sup>2<\/sup> + 3k \u2212 8<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<b>REASONING<\/b> Determine whether each polynomial is factored completely. If not, factor completely.<br \/>\na. 7z<sup>4<\/sup>(2z<sup>2<\/sup> \u2212 z \u2212 6)<br \/>\nb. (2 \u2212 n)(n<sup>2<\/sup> + 6n)(3n \u2212 11)<br \/>\nc. 3(4y \u2212 5)(9y<sup>2<\/sup> \u2212 6y \u2212 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47687\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-65.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 65\" width=\"542\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-65.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-65-300x96.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 66.<br \/>\n<b>PROBLEM SOLVING<\/b> The profit P (in millions of dollars) for a T-shirt manufacturer can be modeled by P = \u2212x<sup>3<\/sup> + 4x<sup>2<\/sup> + x, where x is the number (in millions) of T-shirts produced. Currently the company produces 4 million T-shirts and makes a profit of $4 million. What lesser number of T-shirts could the company produce and still make the same profit?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-44.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 44.1\" width=\"152\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<b>PROBLEM SOLVING<\/b> The profit P (in millions of dollars) for a shoe manufacturer can be modeled by P = \u221221x<sup>3<\/sup> + 46x, where x is the number (in millions) of shoes produced. The company now produces 1 million shoes and makes a profit of $25 million, but it would like to cut back production. What lesser number of shoes could the company produce and still make the same profit?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47688\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-67.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 67\" width=\"597\" height=\"484\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-67.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-67-300x243.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 68.<br \/>\n<b>THOUGHT PROVOKING <\/b>Find a value of k such that \\(\\frac{f(x)}{x-k}\\) has a remainder of 0. Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<b>COMPARING METHODS<\/b> You are taking a test where calculators are not permitted. One question asks you to evaluate g(7) for the function g(x) = x<sup>3<\/sup> \u2212 7x<sup>2<\/sup> \u2212 4x + 28. You use the Factor Theorem and synthetic division and your friend uses direct substitution. Whose method do you prefer? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47689\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-69.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 69\" width=\"567\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-69.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-69-300x47.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 70.<br \/>\n<b>MAKING AN ARGUMENT<\/b> You divide f(x) by (x\u2212a) and find that the remainder does not equal 0. Your friend concludes that f(x) cannot be factored. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<b>CRITICAL THINKING<\/b> What is the value of k such that x\u2212 7 is a factor of h(x) = 2x<sup>3<\/sup> \u2212 13x<sup>2<\/sup> \u2212 kx + 105? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47690\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-71.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 71\" width=\"318\" height=\"317\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-71.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-71-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-71-150x150.png 150w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p>Question 72.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> Use the graph to write an equation of the cubic function in factored form. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 45\" width=\"198\" height=\"184\" \/><br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\n<b>ABSTRACT REASONING<\/b> Factor each polynomial completely.<br \/>\na. 7ac<sup>2<\/sup> + bc<sup>2<\/sup> \u2212 7ad<sup>2<\/sup> \u2212 bd<sup>2<\/sup><br \/>\nb. x<sup>2n<\/sup> \u2212 2x<sup>n<\/sup> + 1<br \/>\nc. a<sup>5<\/sup>b<sup>2<\/sup> \u2212 a<sup>2<\/sup>b<sup>4<\/sup> + 2a<sup>4<\/sup>b \u2212 2ab<sup>3<\/sup> + a<sup>3<\/sup> \u2212 b<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47691\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-73.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 73\" width=\"541\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-73.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-73-300x155.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 74.<br \/>\n<b>REASONING<\/b> The graph of the function f(x) = x<sup>4<\/sup> + 3x<sup>3<\/sup> + 2x<sup>2<\/sup> + x + 3 is shown. Can you use the Factor Theorem to factor f(x)? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> The standard equation of a circle with radius r and center (h, k) is (x \u2212 h)<sup>2<\/sup> + (y \u2212 k)<sup>2<\/sup> = r<sup>2<\/sup>. Rewrite each equation of a circle in standard form. Identify the center and radius of the circle. Then graph the circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-46.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 46\" width=\"177\" height=\"153\" \/><br \/>\na. x<sup>2<\/sup> + 6x + 9 + y<sup>2<\/sup> = 25<br \/>\nb. x<sup>2<\/sup> \u2212 4x + 4 + y<sup>2<\/sup> = 9<br \/>\nc. x<sup>2<\/sup> \u2212 8x + 16 + y<sup>2<\/sup> + 2y + 1 = 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47692\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 75.1\" width=\"408\" height=\"432\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.1.png 408w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.1-283x300.png 283w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47693\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 75.2\" width=\"399\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.2.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.2-300x266.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47694\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 75.3\" width=\"423\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.3.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-75.3-291x300.png 291w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Question 76.<br \/>\n<b>CRITICAL THINKING<\/b> Use the diagram to complete parts (a)\u2013(c).<br \/>\na. Explain why a<sup>3<\/sup> \u2212 b<sup>3<\/sup> is equal to the sum of the volumes of the solids I, II, and III.<br \/>\nb. Write an algebraic expression for the volume of each of the three solids. Leave your expressions in factored form.<br \/>\nc. Use the results from part (a) and part (b) to derive the factoring pattern a<sup>3<\/sup> \u2212 b<sup>3<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 47\" width=\"174\" height=\"154\" \/><br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the quadratic equation by factoring.<\/b>(Section 3.1)<\/p>\n<p>Question 77.<br \/>\nx<sup>2<\/sup> \u2212 x \u2212 30 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47695\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-77.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 77\" width=\"360\" height=\"130\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-77.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-77-300x108.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><\/p>\n<p>Question 78.<br \/>\n2x<sup>2<\/sup> \u2212 10x \u2212 72 = 0<br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n3x<sup>2<\/sup> \u2212 11x + 10 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47696\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-79.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 79\" width=\"364\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-79.png 364w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-79-300x116.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>Question 80.<br \/>\n9x<sup>2<\/sup> \u2212 28x + 3 = 0<br \/>\nAnswer:<\/p>\n<p><b>Solve the quadratic equation by completing the square.(<\/b>Section 3.3)<\/p>\n<p>Question 81.<br \/>\nx<sup>2<\/sup> \u2212 12x + 36 = 144<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47697\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-81.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 81\" width=\"328\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-81.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-81-300x155.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p>Question 82.<br \/>\nx<sup>2<\/sup> \u2212 8x \u2212 11 = 0<br \/>\nAnswer:<\/p>\n<p>Question 83.<br \/>\n3x<sup>2<\/sup> + 30x + 63 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-83.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.4 Question 83\" width=\"361\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-83.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.4-Question-83-300x227.png 300w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><\/p>\n<p>Question 84.<br \/>\n4x<sup>2<\/sup> + 36x \u2212 4 = 0<br \/>\nAnswer:<\/p>\n<h3><a id=\"Polynomial_Functions_Study_Skills\"><\/a>Polynomial Functions Study Skills : Keeping Your Mind Focused<\/h3>\n<p><b>4.1\u20134.4 What Did You Learn?<\/b><\/p>\n<p><b>Core Vocabulary<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-48.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 48\" width=\"706\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-48.png 706w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-48-300x33.png 300w\" sizes=\"(max-width: 706px) 100vw, 706px\" \/><\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 4.1<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 49\" width=\"658\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-49.png 658w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-49-300x26.png 300w\" sizes=\"(max-width: 658px) 100vw, 658px\" \/><\/p>\n<p><b>Section 4.2<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-50.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 50\" width=\"562\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-50.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-50-300x27.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p><b>Section 4.3<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 51\" width=\"610\" height=\"50\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-51.png 610w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-51-300x25.png 300w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><\/p>\n<p><b>Section 4.4<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-52.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 52\" width=\"593\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-52.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-52-300x32.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nDescribe the entry points you used to analyze the function in Exercise 43 on page 164.<\/p>\n<p>Question 2.<br \/>\nDescribe how you maintained oversight in the process of factoring the polynomial in Exercise 49 on page 185.<\/p>\n<p><b>Study Skills<br \/>\nKeeping Your Mind Focused<\/b><\/p>\n<ul>\n<li>When you sit down at your desk, review your notes from the last class.<\/li>\n<li>Repeat in your mind what you are writing in your notes.<\/li>\n<li>When a mathematical concept is particularly difficult, ask your teacher for another example.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-52.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 52.1\" width=\"431\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-52.1.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-52.1-300x216.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<h3><a id=\"Polynomial_Functions_4.1_-_4.4_Quiz\"><\/a>Polynomial Functions 4.1 &#8211; 4.4 Quiz<\/h3>\n<p><b>Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.<\/b>(Section 4.1)<\/p>\n<p>Question 1.<br \/>\nf(x) = 5 + 2x<sup>2<\/sup> \u2212 3x<sup>4<\/sup> \u2212 2x \u2212 x<sup>3<\/sup><\/p>\n<p>Question 2.<br \/>\ng(x) = \\(\\frac{1}{4}\\)x<sup>3<\/sup> + 2x \u2212 3x<sup>2<\/sup> + 1<\/p>\n<p>Question 3.<br \/>\nh(x) = 3 \u2212 6x<sup>3<\/sup> + 4x \u2212 2 + 6x<\/p>\n<p>Question 4.<br \/>\nDescribe the x-values for which<br \/>\n(a) f is increasing or decreasing,<br \/>\n(b) f(x) &gt; 0, and<br \/>\n(c) f(x) &lt; 0. (Section 4.1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 53\" width=\"200\" height=\"186\" \/><\/p>\n<p>Question 5.<br \/>\nWrite an expression for the area and perimeter for the figure shown.(Section 4.2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-54.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 54\" width=\"182\" height=\"163\" \/><\/p>\n<p><b>Perform the indicated operation.<\/b>(Section 4.2)<\/p>\n<p>Question 6.<br \/>\n(7x<sup>2<\/sup> \u2212 4) \u2212 (3x<sup>2<\/sup> \u2212 5x + 1)<\/p>\n<p>Question 7.<br \/>\n(x<sup>2<\/sup> \u2212 3x + 2)(3x \u2212 1)<\/p>\n<p>Question 8.<br \/>\n(x \u2212 1)(x + 3)(x \u2212 4)<\/p>\n<p>Question 9.<br \/>\nUse Pascal\u2019s Triangle to expand (x + 2)<sup>5<\/sup>. (Section 4.2)<\/p>\n<p>Question 10.<br \/>\nDivide 4x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 5x + 8 by x<sup>2<\/sup> \u2212 2x \u2212 1. (Section 4.3)<\/p>\n<p><b>Factor the polynomial completely.<\/b>(Section 4.4)<\/p>\n<p>Question 11.<br \/>\na<sup>3<\/sup> \u2212 2a<sup>2<\/sup> \u2212 8a<\/p>\n<p>Question 12.<br \/>\n8m<sup>3<\/sup> + 27<\/p>\n<p>Question 13.<br \/>\nz<sup>3<\/sup> + z<sup>2<\/sup> \u2212 4z \u2212 4<\/p>\n<p>Question 14.<br \/>\n49b<sup>4<\/sup> \u2212 64<\/p>\n<p>Question 15.<br \/>\nShow that x + 5 is a factor of f(x) = x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 23x + 60. Then factor f(x) completely. (Section 4.4)<\/p>\n<p>Question 16.<br \/>\nThe estimated price P (in cents) of stamps in the United States can be modeled by the polynomial function P(t)= 0.007t<sup>3<\/sup> \u2212 0.16t<sup>2<\/sup> + 1t + 17, where t represents the number of years since 1990. (Section 4.1)<br \/>\na. Use a graphing calculator to graph the function for the interval 0 \u2264 t \u2264 20. Describe the behavior of the graph on this interval.<br \/>\nb. What was the average rate of change in the price of stamps from 1990 to 2010?<\/p>\n<p>Question 17.<br \/>\nThe volume V (in cubic feet) of a rectangular wooden crate is modeled by the function V(x) = 2x<sup>3<\/sup> \u2212 11x<sup>2<\/sup> + 12x, where x is the width (in feet) of the crate. Determine the values of x for which the model makes sense. Explain your reasoning. (Section 4.4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-55.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 55\" width=\"200\" height=\"206\" \/><\/p>\n<h3><a id=\"Lesson_4.5_Solving_Polynomial_Equations\"><\/a>Lesson 4.5 Solving Polynomial Equations<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you determine whether a polynomial equation has a repeated solution?<\/p>\n<p><b>EXPLORATION 1<br \/>\nCubic Equations and Repeated Solutions<br \/>\nWork with a partner. <\/b>Some cubic equations have three distinct solutions. Others have repeated solutions. Match each cubic polynomial equation with the graph of its related polynomial function. Then solve each equation. For those equations that have repeated solutions, describe the behavior of the related function near the repeated zero using the graph or a table of values.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-56.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 56\" width=\"253\" height=\"230\" \/><br \/>\na. x<sup>3<\/sup> \u2212 6x<sup>2<\/sup> + 12x \u2212 8 = 0<br \/>\nb. x<sup>3<\/sup> + 3x<sup>2<\/sup> + 3x + 1 = 0<br \/>\nc. x<sup>3<\/sup>\u2212 3x + 2 = 0<br \/>\nd. x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 2x = 0<br \/>\ne. x<sup>3<\/sup> \u2212 3x \u2212 2 = 0<br \/>\nf. x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + 2x = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-57.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 57\" width=\"543\" height=\"450\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-57.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-57-300x249.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nQuartic Equations and Repeated Solutions<br \/>\nWork with a partner. <\/b>Determine whether each quartic equation has repeated solutions using the graph of the related quartic function or a table of values. Explain your reasoning. Then solve each equation.<br \/>\na. x<sup>4<\/sup> \u2212 4x<sup>3<\/sup> + 5x<sup>2<\/sup> \u2212 2x = 0<br \/>\nb. x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + 2x = 0<br \/>\nc. x<sup>4<\/sup> \u2212 4x<sup>3<\/sup> + 4x<sup>2<\/sup> = 0<br \/>\nd. x<sup>4<\/sup> + 3x<sup>3<\/sup> = 0<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you determine whether a polynomial equation has a repeated solution?<\/p>\n<p>Question 4.<br \/>\nWrite a cubic or a quartic polynomial equation that is different from the equations in Explorations 1 and 2 and has a repeated solution.<\/p>\n<p><b>4.5 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Solve the equation.<\/b><\/p>\n<p>Question 1.<br \/>\n4x<sup>4<\/sup> \u2212 40x<sup>2<\/sup> + 36 = 0<\/p>\n<p>Question 2.<br \/>\n2x<sup>5<\/sup> + 24x = 14x<sup>3<\/sup><\/p>\n<p><b>Find the zeros of the function. Then sketch a graph of the function.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = 3x<sup>4<\/sup> \u2212 6x<sup>2<\/sup> + 3<\/p>\n<p>Question 4.<br \/>\nf(x) = x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 6x<\/p>\n<p>Question 5.<br \/>\nFind all real solutions of x<sup>3<\/sup> \u2212 5x<sup>2<\/sup> \u2212 2x + 24 = 0.<\/p>\n<p>Question 6.<br \/>\nFind all real zeros of f(x) = 3x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> \u2212 37x<sup>2<\/sup> + 24x + 12.<\/p>\n<p>Question 7.<br \/>\nWrite a polynomial function f of least degree that has rational coefficients, aleading coefficient of 1, and the zeros 4 and 1 \u2212 \\(\\sqrt{5}\\).<\/p>\n<h3><a id=\"Solving_Polynomial_Equations_4.5_Exercises\"><\/a>Solving Polynomial Equations 4.5 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> If a polynomial function f has integer coefficients, then every rational solution of f(x) = 0 has the form \\(\\frac{p}{q}\\), where p is a factor of the _____________ and q is a factor of the _____________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47699\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 1\" width=\"575\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-1-300x66.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>DIFFERENT WORDS, SAME QUESTION<\/b> Which is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-58.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 58\" width=\"550\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-58.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-58-300x69.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u201312, solve the equation.<\/b><\/p>\n<p>Question 3.<br \/>\nz<sup>3<\/sup> \u2212 z<sup>2<\/sup> \u2212 12z = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47700\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 3\" width=\"410\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-3.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-3-300x98.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><\/p>\n<p>Question 4.<br \/>\na<sup>3<\/sup> \u2212 4a<sup>2<\/sup> + 4a = 0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n2x<sup>4<\/sup> \u2212 4x<sup>3<\/sup> = \u22122x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47701\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 5\" width=\"329\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-5.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-5-300x156.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Question 6.<br \/>\nv<sup>3<\/sup> \u2212 2v<sup>2<\/sup> \u2212 16v = \u2212 32<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n5w<sup>3<\/sup> = 50w<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47702\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 7\" width=\"484\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-7.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-7-300x110.png 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><\/p>\n<p>Question 8.<br \/>\n9m<sup>5<\/sup> = 27m<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n2c<sup>4<\/sup> \u2212 6c<sup>3<\/sup> = 12c<sup>2<\/sup> \u2212 36c<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47703\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 9\" width=\"511\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-9.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-9-300x141.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 10.<br \/>\np<sup>4<\/sup> + 40 = 14p<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n12n<sup>2<\/sup> + 48n = \u2212n<sup>3<\/sup> \u2212 64<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47704\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 11\" width=\"348\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-11.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-11-300x116.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 12.<br \/>\ny<sup>3<\/sup> \u2212 27 = 9y<sup>2<\/sup> \u2212 27y<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 13\u201320, find the zeros of the function. Then sketch a graph of the function.<\/b><\/p>\n<p>Question 13.<br \/>\nh(x) = x<sup>4<\/sup> + x<sup>3<\/sup> \u2212 6x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47705\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 13\" width=\"419\" height=\"443\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-13.png 419w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-13-284x300.png 284w\" sizes=\"(max-width: 419px) 100vw, 419px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 18x<sup>2<\/sup> + 81<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\np(x) = x<sup>6<\/sup> \u2212 11x<sup>5<\/sup> + 30x<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47706\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 15\" width=\"420\" height=\"409\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-15.png 420w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-15-300x292.png 300w\" sizes=\"(max-width: 420px) 100vw, 420px\" \/><\/p>\n<p>Question 16.<br \/>\ng(x) = \u22122x<sup>5<\/sup> + 2x<sup>4<\/sup> + 40x<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ng(x) = \u22124x<sup>4<\/sup> + 8x<sup>3<\/sup> + 60x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47707\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 17\" width=\"423\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-17.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-17-267x300.png 267w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Question 18.<br \/>\nh(x) = \u2212x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> + 15x<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nh(x) = \u2212x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + 9x + 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47708\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 19\" width=\"453\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-19.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-19-257x300.png 257w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 20.<br \/>\np(x) = x<sup>3<\/sup> \u2212 5x<sup>2<\/sup> \u2212 4x + 20<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<b>USING EQUATIONS<\/b> According to the Rational Root Theorem, which is not a possible solution of the equation 2x<sup>4<\/sup> \u2212 5x<sup>3<\/sup> + 10x<sup>2<\/sup> \u2212 9 = 0?<br \/>\nA. \u22129<br \/>\nB. \u2212\\([\\frac{1}{2}\/latex]<br \/>\nC. [latex][\\frac{5}{2}\/latex]<br \/>\nD. 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47709\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 21\" width=\"245\" height=\"29\" \/><\/p>\n<p>Question 22.<br \/>\n<b>USING EQUATIONS <\/b>According to the Rational Root Theorem, which is not a possible zero of the function f(x) = 40x<sup>5<\/sup> \u2212 42x<sup>4<\/sup> \u2212 107x<sup>3<\/sup> + 107x<sup>2<\/sup> + 33x \u2212 36?<br \/>\nA. \u2212[latex][\\frac{2}{3}\/latex]<br \/>\nB. \u2212 [latex][\\frac{3}{8}\/latex]<br \/>\nC. [latex][\\frac{3}{4}\/latex]<br \/>\nD. [latex][\\frac{4}{5}\/latex]<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 23 and 24, describe and correct the error in listing the possible rational zeros of the function.<\/b><\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-59.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 59\" width=\"376\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-59.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-59-300x97.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47710\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 23\" width=\"585\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-23.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-23-300x42.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-60.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 60\" width=\"376\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-60.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-60-300x100.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 25\u201332, find all the real solutions of the equation.<\/b><\/p>\n<p>Question 25.<br \/>\nx<sup>3<\/sup> + x<sup>2<\/sup> \u2212 17x + 15 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47711\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 25\" width=\"579\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-25.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-25-300x160.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 26.<br \/>\nx<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 5x + 6 = 0<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nx<sup>3<\/sup> \u2212 10x<sup>2<\/sup> + 19x + 30 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47712\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 27\" width=\"567\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-27.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-27-300x173.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 28.<br \/>\nx<sup>3<\/sup> + 4x<sup>2<\/sup> \u2212 11x \u2212 30 = 0<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nx<sup>3<\/sup> \u2212 6x<sup>2<\/sup> \u2212 7x + 60 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 29\" width=\"556\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-29.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-29-300x180.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 30.<br \/>\nx<sup>3<\/sup> \u2212 16x<sup>2<\/sup> + 55x + 72 = 0<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n2x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> \u2212 50x \u2212 24 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47714\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 31\" width=\"564\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-31.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-31-300x178.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 32.<br \/>\n3x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 38x + 24 = 0<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 33\u201338, find all the real zeros of the function.<\/b><\/p>\n<p>Question 33.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 23x + 60<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47715\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 33\" width=\"565\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-33.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-33-300x177.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 34.<br \/>\ng(x) = x<sup>3<\/sup> \u2212 28x \u2212 48<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nh(x) = x<sup>3<\/sup> + 10x<sup>2<\/sup> + 31x + 30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47716\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 35\" width=\"580\" height=\"333\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-35.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-35-300x172.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 36.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 14x<sup>2<\/sup> + 55x \u2212 42<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\np(x) = 2x<sup>3<\/sup> \u2212x<sup>2<\/sup> \u2212 27x + 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47717\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 37\" width=\"565\" height=\"352\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-37.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-37-300x187.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 38.<br \/>\ng(x) = 3x<sup>3<\/sup> \u2212 25x<sup>2<\/sup> + 58x \u2212 40<br \/>\nAnswer:<\/p>\n<p><b>USING TOOLS In Exercises 39 and 40, use the graph to shorten the list of possible rational zeros of the function. Then find all real zeros of the function.<\/b><\/p>\n<p>Question 39.<br \/>\nf(x) = 4x<sup>3<\/sup> \u2212 20x + 16<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-61.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 61\" width=\"185\" height=\"173\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47718\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 39\" width=\"558\" height=\"589\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-39.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-39-284x300.png 284w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 40.<br \/>\nf(x) = 4x<sup>3<\/sup> \u2212 49x \u2212 60<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-62.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 62\" width=\"191\" height=\"171\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 41\u201346, write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros.<\/b><\/p>\n<p>Question 41.<br \/>\n\u22122, 3, 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47719\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 41\" width=\"397\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-41.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-41-300x101.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><\/p>\n<p>Question 42.<br \/>\n\u22124, \u22122, 5<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n\u22122, 1 + [latex]\\sqrt{7}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47720\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 43\" width=\"459\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-43.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-43-300x161.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 44.<br \/>\n4, 6 \u2212 \\(\\sqrt{7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n\u22126, 0, 3 \u2212\\(\\sqrt{5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47721\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 45\" width=\"467\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-45.png 467w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-45-300x179.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>Question 46.<br \/>\n0, 5, \u22125 + \\(\\sqrt{8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>COMPARING METHODS<\/b> Solve the equation x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> \u2212 9x + 36 = 0 using two different methods. Which method do you prefer? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47722\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-47.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 47.1\" width=\"575\" height=\"445\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-47.1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-47.1-300x232.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47723\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-47.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 47.2\" width=\"579\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-47.2.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-47.2-300x120.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>REASONING<\/b> Is it possible for a cubic function to have more than three real zeros? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>PROBLEM SOLVING<\/b> At a factory, molten glass is poured into molds to make paperweights. Each mold is a rectangular prism with a height 3 centimeters greater than the length of each side of its square base. Each mold holds 112 cubic centimeters of glass. What are the dimensions of the mold?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47724\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 49\" width=\"591\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-49.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-49-300x145.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>MATHEMATICAL CONNECTIONS <\/b>The volume of the cube shown is 8 cubic centimeters.<br \/>\na. Write a polynomial equation that you can use to find the value of x.<br \/>\nb. Identify the possible rational solutions of the equation in part (a).<br \/>\nc. Use synthetic division to find a rational solution of the equation. Show that no other real solutions exist.<br \/>\nd. What are the dimensions of the cube?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-63.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 63\" width=\"163\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<b>PROBLEM SOLVING<\/b> Archaeologists discovered a huge hydraulic concrete block at the ruins of Caesarea with a volume of 945 cubic meters. The block is x meters high by 12x \u2212 15 meters long by 12x \u2212 21 meters wide. What are the dimensions of the block?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-64.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 64\" width=\"241\" height=\"177\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47725\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 51\" width=\"577\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-51.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-51-300x121.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend claims that when a polynomial function has a leading coefficient of 1 and the coefficients are all integers, every possible rational zero is an integer. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>During a 10-year period, the amount (in millions of dollars) of athletic equipment Esold domestically can be modeled by E(t) = \u221220t<sup>3<\/sup> + 252t<sup>2<\/sup> \u2212 280t + 21,614, where t is in years.<br \/>\na. Write a polynomial equation to find the year when about $24,014,000,000 of athletic equipment is sold.<br \/>\nb. List the possible whole-number solutions of the equation in part (a). Consider the domain when making your list of possible solutions.<br \/>\nc. Use synthetic division to find when $24,014,000,000 of athletic equipment is sold.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47726\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 53\" width=\"575\" height=\"365\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-53.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-53-300x190.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>THOUGHT PROVOKING<\/b> Write a third or fourth degree polynomial function that has zeros at \u00b1 \\(\\frac{3}{4}\\). Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>You are designing a marble basin that will hold a fountain for a city park. The sides and bottom of the basin should be 1 foot thick. Its outer length should be twice its outer width and outer height. What should the outer dimensions of the basin be if it is to hold 36 cubic feet of water?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-65.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 65\" width=\"173\" height=\"143\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47727\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 55\" width=\"564\" height=\"301\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-55.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-55-300x160.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 56.<br \/>\n<b>HOW DO YOU SEE IT?<\/b> Use the information in the graph to answer the questions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-66.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 66\" width=\"230\" height=\"178\" \/><br \/>\na. What are the real zeros of the function f ?<br \/>\nb. Write an equation of the quartic function in factored form.<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<b>REASONING <\/b>Determine the value of k for each equation so that the given x-value is a solution.<br \/>\na. x<sup>3<\/sup> \u2212 6x<sup>2<\/sup> \u2212 7x + k = 0; x = 4<br \/>\nb. 2x<sup>3<\/sup> + 7x<sup>2<\/sup> \u2212 kx \u2212 18 = 0; x = \u22126<br \/>\nc. kx<sup>3<\/sup> \u2212 35x<sup>2<\/sup> + 19x + 30 = 0; x = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47728\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 57\" width=\"428\" height=\"587\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-57.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-57-219x300.png 219w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Question 58.<br \/>\n<b>WRITING EQUATIONS<\/b> Write a polynomial function gof least degree that has rational coefficients, a leading coefficient of 1, and the zeros \u22122 + \\(\\sqrt{7}\\) and 3 + \\(\\sqrt{2}\\).<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 59\u201362, solve f(x) = g(x) by graphing and algebraic methods.<\/b><\/p>\n<p>Question 59.<br \/>\nf(x) = x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 x \u2212 1; g(x) = \u2212x + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47729\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 59\" width=\"271\" height=\"370\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-59.png 271w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-59-220x300.png 220w\" sizes=\"(max-width: 271px) 100vw, 271px\" \/><\/p>\n<p>Question 60.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 5x<sup>3<\/sup> + 2x<sup>2<\/sup> + 8x; g(x) = \u2212x<sup>2<\/sup> + 6x \u2212 8<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> + 4x; g(x) = \u22122x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-61.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 61\" width=\"326\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-61.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-61-265x300.png 265w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/p>\n<p>Question 62.<br \/>\nf(x) = x<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 11x<sup>2<\/sup> \u2212 12x + 36;<br \/>\ng(x) = \u2212x<sup>2<\/sup> \u2212 6x \u2212 9<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>You are building a pair of ramps for a loading platform. The left ramp is twice as long as the right ramp. If 150 cubic feet of concrete are used to build the ramps, what are the dimensions of each ramp?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-67.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 67\" width=\"388\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-67.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-67-300x102.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-63.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 63\" width=\"608\" height=\"510\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-63.png 608w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-63-300x252.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>Question 64.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>Some ice sculptures are made by filling a mold and then freezing it. You are making an ice mold for a school dance. It is to be shaped like a pyramid with a height 1 foot greater than the length of each side of its square base. The volume of the ice sculpture is 4 cubic feet. What are the dimensions of the mold?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-68.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 68\" width=\"148\" height=\"127\" \/><br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<b>ABSTRACT REASONING <\/b>Let a<sub>n<\/sub> be the leading coefficient of a polynomial function f and a<sub>0<\/sub> be the constant term. If a<sub>n<\/sub> has r factors and a<sub>0<\/sub> has s factors, what is the greatest number of possible rational zeros of f that can be generated by the Rational Zero Theorem? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-65.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 65\" width=\"573\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-65.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-65-300x45.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.<\/b>(Section 4.1)<\/p>\n<p>Question 66.<br \/>\nh(x) = \u22123x<sub>2<\/sub> + 2x \u2212 9 + \\(\\sqrt{4}\\)x<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\ng(x) = 2x<sup>3<\/sup> \u2212 7x<sup>2<\/sup> \u2212 3x \u2212 1 + x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-67.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 67\" width=\"572\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-67.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-67-300x31.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 68.<br \/>\nf(x) = \\(\\frac{1}{3}\\)x<sup>2<\/sup> + 2x<sup>3<\/sup> \u2212 4x<sup>4<\/sup> \u2212 \\(\\sqrt{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\np(x) = 2x \u2212 5x<sup>3<\/sup> + 9x<sup>2<\/sup> + \\(\\sqrt[4]{x}\\) + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-69.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 69\" width=\"537\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-69.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-69-300x35.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p><b>Find the zeros of the function.<\/b>(Section 3.2)<\/p>\n<p>Question 70.<br \/>\nf(x) = 7x<sup>2<\/sup> + 42<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\ng(x) = 9x<sup>2<\/sup> + 81<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-71.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 71\" width=\"290\" height=\"172\" \/><\/p>\n<p>Question 72.<br \/>\nh(x) = 5x<sup>2<\/sup> + 40<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\nf(x) = 8x<sup>2<\/sup> \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-73.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.5 Question 73\" width=\"313\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-73.png 313w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.5-Question-73-300x229.png 300w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/p>\n<h3><a id=\"Lesson_4.6_The_Fundamental_Theorem_of_Algebra\"><\/a>Lesson 4.6 The Fundamental Theorem of Algebra<\/h3>\n<p><b>Essential Question<\/b><\/p>\n<p>How can you determine whether a polynomial equation has imaginary solutions?<\/p>\n<p><b>EXPLORATION 1<br \/>\nCubic Equations and Imaginary Solutions<br \/>\nWork with a partner. <\/b>Match each cubic polynomial equation with the graph of its related polynomial function. Then find all solutions. Make a conjecture about how you can use a graph or table of values to determine the number and types of solutions of a cubic polynomial equation.<br \/>\na. x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + x + 5 = 0<br \/>\nb. x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 x + 2 = 0<br \/>\nc. x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 4x + 4 = 0<br \/>\nd. x<sup>3<\/sup> + 5x<sup>2<\/sup> + 8x + 6 = 0<br \/>\ne. x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + x \u2212 3 = 0<br \/>\nf. x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + 2x = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-69.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 69\" width=\"544\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-69.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-69-300x250.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nQuartic Equations and Imaginary Solutions<br \/>\nWork with a partner.<\/b> Use the graph of the related quartic function, or a table of values, to determine whether each quartic equation has imaginary solutions. Explain your reasoning. Then find all solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-70.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 70\" width=\"268\" height=\"202\" \/><br \/>\na. x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + 2x = 0<br \/>\nb. x<sup>4<\/sup> \u2212 1 = 0<br \/>\nc. x<sup>4<\/sup> + x<sup>3<\/sup> \u2212 x \u2212 1 = 0<br \/>\nd. x<sup>4<\/sup> \u2212 3x<sup>3<\/sup> + x<sup>2<\/sup> + 3x \u2212 2 = 0<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you determine whether a polynomial equation has imaginary solutions?<\/p>\n<p>Question 4.<br \/>\nIs it possible for a cubic equation to have three imaginary solutions? Explain your reasoning.<\/p>\n<p><b>4.6 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nHow many solutions does the equation x<sup>4<\/sup> + 7x<sup>2<\/sup> \u2212 144 = 0 have?<\/p>\n<p>Question 2.<br \/>\nHow many zeros does the function f(x) = x<sup>3<\/sup> \u2212 5x<sup>2<\/sup> \u2212 8x + 48 have? Find all zeros of the polynomial function.<\/p>\n<p>Question 3.<br \/>\nf(x) = x<sup>3<\/sup> + 7x<sup>2<\/sup> + 16x + 12<\/p>\n<p>Question 4.<br \/>\nf(x) = x<sup>5<\/sup> \u2212 3x<sup>4<\/sup> + 5x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 6x + 4<\/p>\n<p><b>Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.<\/b><\/p>\n<p>Question 5.<br \/>\n\u22121, 4i<\/p>\n<p>Question 6.<br \/>\n3, 1 + i\\(\\sqrt{5}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt{2}\\), 1 \u2212 3i<\/p>\n<p>Question 8.<br \/>\n2, 2i, 4 \u2212 \\(\\sqrt{6}\\)<\/p>\n<p><b>Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function.<\/b><\/p>\n<p>Question 9.<br \/>\nf(x) = x<sup>3<\/sup> + 9x \u2212 25<\/p>\n<p>Question 10.<br \/>\nf(x) = 3x<sup>4<\/sup> \u2212 7x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 13x + 8<\/p>\n<p>Question 11.<br \/>\n<b>WHAT IF? <\/b>In Example 5, what is the tachometer reading when the boat travels 20 miles per hour?<\/p>\n<h3><a id=\"The_Fundamental_Theorem_of_Algebra_4.6_Exercises\"><\/a>The Fundamental Theorem of Algebra 4.6 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> The expressions 5 + i and 5 \u2212 i are _____________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 1\" width=\"525\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-1.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-1-300x19.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING<\/b> How many solutions does the polynomial equation (x + 8)<sup>3<\/sup>(x \u2212 1) = 0 have? Explain.<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p>Question 3.<br \/>\nx<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> + x = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 3\" width=\"566\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-3.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-3-300x32.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 4.<br \/>\n5y<sup>3<\/sup> \u2212 3y<sup>2<\/sup> + 8y = 0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n9t<sup>6<\/sup> \u2212 14t<sup>3<\/sup> + 4t \u2212 1 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 5\" width=\"573\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-5.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-5-300x33.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 6.<br \/>\nf(z) = \u22127z<sup>4<\/sup> + z<sup>2<\/sup> \u2212 25<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ng(s) = 4s<sup>5<\/sup> \u2212 s<sup>3<\/sup> + 2s<sup>7<\/sup> \u2212 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 7\" width=\"583\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-7.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-7-300x31.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 8.<br \/>\nh(x) = 5x<sup>4<\/sup> + 7x<sup>8<\/sup> \u2212 x<sup>12<\/sup><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 9\u201316, find all zeros of the polynomial function.<\/b><\/p>\n<p>Question 9.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 6x<sup>3<\/sup> + 7x<sup>2<\/sup> + 6x \u2212 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 9\" width=\"581\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-9.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-9-300x58.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = x<sup>4<\/sup> + 5x<sup>3<\/sup> \u2212 7x<sup>2<\/sup> \u2212 29x + 30<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ng(x) = x<sup>4<\/sup> \u2212 9x<sup>2<\/sup> \u2212 4x + 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 11\" width=\"591\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-11.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-11-300x119.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 12.<br \/>\nh(x) = x<sup>3<\/sup> + 5x<sup>2<\/sup> \u2212 4x \u2212 20<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\ng(x) = x<sup>4<\/sup> + 4x<sup>3<\/sup> + 7x<sup>2<\/sup> + 16x + 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 13\" width=\"591\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-13.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-13-300x183.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 14.<br \/>\nh(x) = x<sup>4<\/sup> \u2212 x<sup>3<\/sup> + 7x<sup>2<\/sup> \u2212 9x \u2212 18<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ng(x) = x<sup>5<\/sup> + 3x<sup>4<\/sup> \u2212 4x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 12x \u2212 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 15\" width=\"595\" height=\"424\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-15.png 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-15-300x214.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = x<sup>5<\/sup> \u2212 20x<sup>3<\/sup> + 20x<sup>2<\/sup> \u2212 21x + 20<br \/>\nAnswer:<\/p>\n<p><b>ANALYZING RELATIONSHIPS In Exercises 17\u201320, determine the number of imaginary zeros for the function with the given degree and graph. Explain your reasoning.<\/b><\/p>\n<p>Question 17.<br \/>\nDegree: 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-70.1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 70.1\" width=\"180\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 17\" width=\"547\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-17.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-17-300x35.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 18.<br \/>\nDegree: 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-71.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 71\" width=\"182\" height=\"156\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nDegree: 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-72.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 72\" width=\"189\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 19\" width=\"543\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-19.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-19-300x34.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 20.<br \/>\nDegree: 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-73.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 73\" width=\"186\" height=\"152\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 21\u201328, write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.<\/b><\/p>\n<p>Question 21.<br \/>\n\u22125, \u22121, 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 21\" width=\"566\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-21.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-21-300x85.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 22.<br \/>\n\u22122, 1, 3<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n3, 4 + i<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 23\" width=\"580\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-23.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-23-300x183.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 24.<br \/>\n2, 5 \u2212 i<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n4, \u2212\\(\\sqrt{5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 25\" width=\"578\" height=\"252\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-25.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-25-300x131.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 26.<br \/>\n3i, 2 \u2212 i<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n2, 1 + i, 2 \u2212\\(\\sqrt{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 27\" width=\"599\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-27.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-27-300x267.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<p>Question 28.<br \/>\n3, 4 + 2i, 1 + \\(\\sqrt{7}\\)<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 29 and 30, describe and correct the error in writing a polynomial function with rational coefficients and the given zero(s).<\/b><\/p>\n<p>Question 29.<br \/>\nZeros: 2, 1 + i<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-74.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 74\" width=\"351\" height=\"134\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-74.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-74-300x115.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 29\" width=\"529\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-29.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-29-300x155.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 30.<br \/>\nZero: 2 +i<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-75.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 75\" width=\"415\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-75.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-75-300x108.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<b>OPEN-ENDED<\/b> Write a polynomial function of degree 6 with zeros 1, 2, and \u2212i. Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 31\" width=\"440\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-31.png 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-31-300x143.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>Question 32.<br \/>\n<b>REASONING<\/b> Two zeros of f(x) = x<sup>3<\/sup> \u2212 6x<sup>2<\/sup> \u2212 16x + 96 are 4 and \u22124. Explain why the third zero must also be a real number.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 33\u201340, determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function.<\/b><\/p>\n<p>Question 33.<br \/>\ng(x) = x<sup>4<\/sup> \u2212 x<sup>2<\/sup> \u2212 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 33\" width=\"563\" height=\"226\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-33.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-33-300x120.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 34.<br \/>\ng(x) = \u2212x<sup>3<\/sup> + 5x<sup>2<\/sup> + 12<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ng(x) = x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> + 8x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 35\" width=\"567\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-35.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-35-300x140.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 36.<br \/>\ng(x) = x<sup>5<\/sup> \u2212 2x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + 6<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ng(x) = x<sup>5<\/sup> \u2212 3x<sup>3<\/sup> + 8x \u2212 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 37\" width=\"556\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-37.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-37-300x185.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 38.<br \/>\ng(x) = x<sup>5<\/sup> + 7x<sup>4<\/sup> \u2212 4x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + 9x \u2212 15<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\ng(x) = x<sup>6<\/sup> + x<sup>5<\/sup> \u2212 3x<sup>4<\/sup> + x<sup>3<\/sup> + 5x<sup>2<\/sup> + 9x \u2212 18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 39\" width=\"552\" height=\"340\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-39.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-39-300x185.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 40.<br \/>\ng(x) = x<sup>7<\/sup> + 4x<sup>4<\/sup> \u2212 10x + 25<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<b>REASONING <\/b>Which is not a possible classification of zeros for f(x) = x<sup>5<\/sup> \u2212 4x<sup>3<\/sup> + 6x<sup>2<\/sup> + 2x \u2212 6? Explain.<br \/>\nA. three positive real zeros, two negative real zeros, and zero imaginary zeros<br \/>\nB. three positive real zeros, zero negative real zeros, and two imaginary zeros<br \/>\nC. one positive real zero, four negative real zeros, and zero imaginary zeros<br \/>\nD. one positive real zero, two negative real zeros, and two imaginary zeros<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 41\" width=\"589\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-41.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-41-300x30.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 42.<br \/>\n<b>USING STRUCTURE<\/b> Use Descartes\u2019s Rule of Signs to determine which function has at least 1 positive real zero.<br \/>\nA. f(x) = x<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 9x<sup>2<\/sup> \u2212 2x &#8211; 8<br \/>\nB. f(x) = x<sup>4<\/sup> + 4x<sup>3<\/sup> + 8x<sup>2<\/sup> + 16x + 16<br \/>\nC. f(x) = \u2212x<sup>4<\/sup> \u2212 5x<sup>2<\/sup> \u2212 4<br \/>\nD. f(x) = x<sup>4<\/sup> + 4x<sup>3<\/sup> + 7x<sup>2<\/sup> + 12x + 12<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> From 1890 to 2000, the American Indian, Eskimo, and Aleut population P (in thousands) can be modeled by the function P = 0.004t<sup>3<\/sup> \u2212 0.24t<sup>2<\/sup> + 4.9t + 243, where t is the number of years since 1890. In which year did the population first reach 722,000?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 43\" width=\"577\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-43.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-43-300x232.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 44.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> Over a period of 14 years, the number N of inland lakes infested with zebra mussels in a certain state can be modeled by<br \/>\nN = \u22120.0284t<sup>4<\/sup> + 0.5937t<sup>3<\/sup> \u2212 2.464t<sup>2<\/sup> + 8.33t \u2212 2.5<br \/>\nwhere t is time (in years). In which year did the number of infested inland lakes first reach 120?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-76.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 76\" width=\"307\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-76.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-76-300x172.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>For the 12 years that a grocery store has been open, its annual revenue R (in millions of dollars) can be modeled by the function<br \/>\nR = 0.0001(\u2212t<sup>4<\/sup> + 12t<sup>3<\/sup> \u2212 77t<sup>2<\/sup> + 600t + 13,650)where t is the number of years since the store opened. In which year(s) was the revenue $1.5 million?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-77.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 77\" width=\"309\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-77.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-77-300x203.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 45\" width=\"599\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-45.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-45-300x261.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<p>Question 46.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend claims that 2 \u2212 i is a complex zero of the polynomial function f(x) = x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> + 2x + 5i, but that its conjugate is not a zero. You claim that both 2 \u2212 i and its conjugate must be zeros by the Complex Conjugates Theorem. Who is correct? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> A solid monument with the dimensions shown is to be built using 1000 cubic feet of marble. What is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-78.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 78\" width=\"273\" height=\"174\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 47\" width=\"585\" height=\"559\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-47.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-47-300x287.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>THOUGHT PROVOKING <\/b>Write and graph a polynomial function of degree 5 that has all positive or negative real zeros. Label each x-intercept. Then write the function in standard form.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>WRITING <\/b>The graph of the constant polynomial function f(x) = 2 is a line that does not have any x-intercepts. Does the function contradict the Fundamental Theorem of Algebra? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 49\" width=\"587\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-49.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-49-300x59.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>The graph represents a polynomial function of degree 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-79.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 79\" width=\"188\" height=\"176\" \/><br \/>\na. How many positive real zeros does the function have? negative real zeros? imaginary zeros?<br \/>\nb. Use Descartes\u2019s Rule of Signs and your answers in part (a) to describe the possible sign changes in the coefficients of f(x).<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<b>FINDING A PATTERN<\/b> Use a graphing calculator to graph the function f(x) = (x + 3)<sup>n<\/sup> for n = 2, 3, 4, 5, 6, and 7.<br \/>\na. Compare the graphs when n is even and n is odd.<br \/>\nb. Describe the behavior of the graph near the zero x = \u22123 as n increases.<br \/>\nc. Use your results from parts (a) and (b) to describe the behavior of the graph of g(x) = (x \u2212 4)<sup>20<\/sup> near x = 4.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-51.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 51.1\" width=\"567\" height=\"535\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-51.1.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-51.1-300x283.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-51.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 51.2\" width=\"566\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-51.2.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-51.2-300x112.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>DRAWING CONCLUSIONS<\/b> Find the zeros of each function.<br \/>\nf(x) = x<sup>5<\/sup> \u2212 5x + 6<br \/>\ng(x) = x<sup>3<\/sup> \u2212 7x + 6<br \/>\nh(x) = x<sup>4<\/sup> + 2x<sup>3<\/sup> + x<sup>2<\/sup> + 8x \u2212 12<br \/>\nk(x) = x<sup>5<\/sup> \u2212 3x<sup>4<\/sup> \u2212 9x<sup>3<\/sup> + 25x<sup>2<\/sup> \u2212 6x<br \/>\na. Describe the relationship between the sum of the zeros of a polynomial function and the coefficients of the polynomial function.<br \/>\nb. Describe the relationship between the product of the zeros of a polynomial function and the coefficients of the polynomial function.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>PROBLEM SOLVING<\/b> You want to save money so you can buy a used car in four years. At the end of each summer, you deposit $1000 earned from summer jobs into your bank account. The table shows the value of your deposits over the four-year period. In the table, g is the growth factor 1 + r, where r is the annual interest rate expressed as a decimal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-80.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 80\" width=\"392\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-80.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-80-300x143.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\na. Copy and complete the table.<br \/>\nb. Write a polynomial function that gives the value v of your account at the end of the fourth summer in terms of g.<br \/>\nc. You want to buy a car that costs about $4300. What growth factor do you need to obtain this amount? What annual interest rate do you need?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-53.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 53.1\" width=\"582\" height=\"642\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-53.1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-53.1-272x300.png 272w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Describe the transformation of f(x) = x<sup>2<\/sup> represented by g. Then graph each function.<\/b> (Section 2.1)<\/p>\n<p>Question 54.<br \/>\ng(x) = \u22123x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\ng(x) = (x \u2212 4)<sup>2<\/sup> + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 55\" width=\"586\" height=\"418\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-55.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-55-300x214.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 56.<br \/>\ng(x) = \u2212(x \u2212 1)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\ng(x) = 5(x + 4)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 57\" width=\"507\" height=\"347\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-57.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-57-300x205.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p><b>Write a function g whose graph represents the indicated transformation of the graph of f.<\/b>(Sections 1.2and 2.1)<\/p>\n<p>Question 58.<br \/>\nf(x) = x; vertical shrink by a factor of \\(\\frac{1}{3}\\) and a reflection in the y-axis<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\nf(x) = | x + 1 \u2223\u2212 3; horizontal stretch by a factor of 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.6 Question 59\" width=\"534\" height=\"150\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-59.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.6-Question-59-300x84.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 60.<br \/>\nf(x) = x<sup>2<\/sup>; reflection in the x-axis, followed by a translation 2 units right and 7 units up<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_4.7_Transformations_of_Polynomial_Functions\"><\/a>Lesson 4.7 Tranformations of Polynomial Functions<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you transform the graph of a polynomial function?<\/p>\n<p><b>EXPLORATION 1<br \/>\nTransforming the Graph of a Cubic Function<br \/>\nWork with a partner. <\/b>The graph of the cubic function f(x) = x<sup>3<\/sup> is shown. The graph of each cubic function g represents a transformation of the graph of f. Write a rule for g. Use a graphing calculator to verify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-81.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 81\" width=\"220\" height=\"150\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-81.1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 81.1\" width=\"524\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-81.1.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-81.1-300x176.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p><b>EXPLORATION 2<br \/>\nTransforming the Graph of a Quartic Function<br \/>\nWork with a partner. <\/b>The graph of the quartic function f(x) = x<sup>4<\/sup> is shown. The graph of each quartic function g represents a transformation of the graph of f. Write a rule for g. Use a graphing calculator to verify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-82.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 82\" width=\"204\" height=\"162\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-82.1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 82.1\" width=\"522\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-82.1.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-82.1-300x99.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 3.<br \/>\nHow can you transform the graph of a polynomial function?<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-4-Polynomial-Functions-83.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 4 Polynomial Functions 83\" width=\"255\" height=\"258\" \/><br \/>\n<span style=\"font-size: 16px;\">Question 4.<\/span><\/p>\n<p>Describe the transformation of f(x) = x<sup>4<\/sup> represented by g(x) = (x + 1)<sup>4<\/sup> + 3. Then graph g.<\/p>\n<p><b>4.7 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p>Question 1.<br \/>\nDescribe the transformation of f(x) = x<sup>4<\/sup> represented by g(x) = (x \u2212 3)<sup>4<\/sup> \u2212 1. Then graph each function.<\/p>\n<p>Question 2.<br \/>\nDescribe the transformation of f(x) = x<sup>3<\/sup> represented by g(x) = 4(x + 2)<sup>3<\/sup>. Then graph each function.<\/p>\n<p>Question 3.<br \/>\nLet f(x) = x<sup>5<\/sup> \u2212 4x + 6 and g(x) = \u2212f(x). Write a rule for g and then graph each function. Describe the graph of g as a transformation of the graph of f.<\/p>\n<p>Question 4.<br \/>\nLet the graph of g be a horizontal stretch by a factor of 2, followed by a translation 3 units to the right of the graph of f(x) = 8x<sup>3<\/sup> + 3. Write a rule for g.<\/p>\n<p>Question 5.<br \/>\n<b>WHAT IF?<\/b> In Example 5, the height of the pyramid is 6x, and the volume (in cubic feet) is represented by V(x) = 2x<sup>3<\/sup>. Write a rule for W. Find and interpret W(7).<\/p>\n<h3><a id=\"Transformations_of_Polynomial_Functions_4.7_Exercises\"><\/a>Tranformations of Polynomial Functions 4.7 Exercises<\/h3>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> The graph of f(x) = (x + 2)<sup>3<\/sup> is a ____________ translation of the graph of f(x) = x<sup>3<\/sup>.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 1\" width=\"562\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-1.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-1-300x32.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>VOCABULARY <\/b>Describe how the vertex form of quadratic functions is similar to the form f(x) = a(x \u2212 h)<sup>3<\/sup> + k for cubic functions.<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 3\u20136, describe the transformation of f represented by g. Then graph each function.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = x<sup>4<\/sup>, g(x) = x<sup>4<\/sup> + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 3\" width=\"569\" height=\"316\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-3.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-3-300x167.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 4.<br \/>\nf(x) = x<sup>4<\/sup>, g(x) = (x \u2212 5)<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nf(x) = x<sup>5<\/sup>, g(x) = (x \u2212 2)<sup>5<\/sup> \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 5\" width=\"581\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-5.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-5-300x176.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 6.<br \/>\nf(x) = x<sup>6<\/sup>, g(x) = (x + 1)<sup>6<\/sup> \u2212 4<br \/>\nAnswer:<\/p>\n<p><b>ANALYZING RELATIONSHIPS In Exercises 7\u201310, match the function with the correct transformation of the graph of f. Explain your reasoning.<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-84.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 84\" width=\"160\" height=\"144\" \/><\/p>\n<p>Question 7.<br \/>\ny = f(x \u2212 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 7\" width=\"395\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-7.png 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-7-300x27.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Question 8.<br \/>\ny = f(x + 2) + 2<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = f(x \u2212 2) + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 9\" width=\"532\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-9.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-9-300x19.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 10.<br \/>\ny = f(x) \u2212 2<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-39991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-85.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 85\" width=\"397\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-85.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-85-300x224.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><\/p>\n<p><b>In Exercises 11\u201316, describe the transformation of f represented by g. Then graph each function.<\/b><\/p>\n<p>Question 11.<br \/>\nf(x) = x<sup>4<\/sup>, g(x) = \u22122x<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 11\" width=\"568\" height=\"429\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-11.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-11-300x227.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 12.<br \/>\nf(x) = x<sup>6<\/sup>, g(x) = \u22123x<sup>6<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nf(x) = x<sup>3<\/sup>, g(x) = 5x<sup>3<\/sup> + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 13\" width=\"570\" height=\"414\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-13.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-13-300x218.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = x<sup>4<\/sup>, g(x) = \\(\\frac{1}{2}\\)x<sup>4<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nf(x) = x<sup>5<\/sup>, g(x) = \\(\\frac{3}{4}\\)(x + 4)<sup>5<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 15\" width=\"585\" height=\"446\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-15.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-15-300x229.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = x<sup>4<\/sup>, g(x) = (2x)<sup>4<\/sup>\u2212 3<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 17\u201320, write a rule for g and then graph each function. Describe the graph of g as a transformation of the graph of f.<\/b><\/p>\n<p>Question 17.<br \/>\nf(x) = x<sup>4<\/sup> + 1, g(x) = f(x + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 17\" width=\"543\" height=\"421\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-17.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-17-300x233.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 18.<br \/>\nf(x) = x<sup>5<\/sup> \u2212 2x + 3, g(x) = 3f(x)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nf(x) = 2x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> + 6, g(x) = \u2212 \\(\\frac{1}{2}\\)f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 19\" width=\"582\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-19.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-19-300x243.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 20.<br \/>\nf(x) = x<sup>4<\/sup> + x<sup>3<\/sup> \u2212 1, g(x) = f(\u2212x) \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in graphing the function g(x) = (x + 2)<sup>4<\/sup> \u2212 6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-86.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 86\" width=\"296\" height=\"176\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 21\" width=\"518\" height=\"257\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-21.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-21-300x149.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 22.<br \/>\n<b>ERROR ANALYSIS <\/b>Describe and correct the error in describing the transformation of the graph of f(x) = x<sup>5<\/sup> represented by the graph of g(x) = (3x)<sup>5<\/sup>\u2212 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-87.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 87\" width=\"372\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-87.png 372w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-87-300x83.png 300w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 6; translation 3 units left, followed by a reflection in the y-axis<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 23\" width=\"603\" height=\"439\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-23.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-23-300x218.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 24.<br \/>\nf(x) = x<sup>4<\/sup> + 2x + 6; vertical stretch by a factor of 2, followed by a translation 4 units right<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nf(x) = x<sup>3<\/sup> + 2x<sup>2<\/sup> \u2212 9; horizontal shrink by a factor of \\(\\frac{1}{3}\\) and a translation 2 units up, followed by a reflection in the x-axis<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 25\" width=\"606\" height=\"363\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-25.png 606w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-25-300x180.png 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = 2x<sup>5<\/sup> \u2212 x<sup>3<\/sup> + x<sup>2<\/sup> + 4; reflection in the y-axis and a vertical stretch by a factor of 3, followed by a translation 1 unit down<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The volume V(in cubic feet) of the pyramid is given by V(x) = x<sup>3<\/sup> \u2212 4x. The function W(x) = V(3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards. Write a rule for W. Find and interpret W(5).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-88.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 88\" width=\"213\" height=\"111\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 27\" width=\"514\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-27.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-27-300x155.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 28.<br \/>\n<b>MAKING AN ARGUMENT<\/b> The volume of a cube with side length x is given by V(x) = x<sup>3<\/sup>. Your friend claims that when you divide the volume in half, the volume decreases by a greater amount than when you divide each side length in half. Is your friend correct? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<b>OPEN-ENDED<\/b> Describe two transformations of the graph of f(x) = x<sup>5<\/sup> where the order in which the transformations are performed is important. Then describe two transformations where the order is not important. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 29\" width=\"585\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-29.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-29-300x87.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 30.<br \/>\n<b>THOUGHT PROVOKING<\/b> Write and graph a transformation of the graph of f(x) = x<sup>5<\/sup> \u2212 3x<sup>4<\/sup> + 2x \u2212 4 that results in a graph with a y-intercept of \u22122.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<b>PROBLEM SOLVING <\/b>A portion of the path that a hummingbird flies while feeding can be modeled by the function<br \/>\nf(x) = \u2212\\(\\frac{1}{5}\\)x(x \u2212 4)2(x \u2212 7), 0 \u2264 x \u2264 7 w<br \/>\nhere x is the horizontal distance (in meters) and f(x) is the height (in meters). The hummingbird feeds each time it is at ground level.<br \/>\na. At what distances does the hummingbird feed?<br \/>\nb. A second hummingbird feeds 2 meters farther away than the first hummingbird and flies twice as high. Write a function to model the path of the second hummingbird.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-89.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 89\" width=\"279\" height=\"191\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 31\" width=\"599\" height=\"367\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-31.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-31-300x184.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<p>Question 32.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>Determine the real zeros of each function. Then describe the transformation of the graph of f that results in the graph of g.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-90.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 90\" width=\"192\" height=\"186\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> Write a function V for the volume (in cubic yards) of the right circular cone shown. Then write a function W that gives the volume (in cubic yards) of the cone when x is measured in feet. Find and interpret W(3).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-91.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 91\" width=\"168\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 33\" width=\"511\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-33.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-33-294x300.png 294w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Find the minimum value or maximum value of the function. Describe the domain and range of the function, and where the function is increasing and decreasing.<\/b>(Section 2.2)<\/p>\n<p>Question 34.<br \/>\nh(x) = (x + 5)<sup>2<\/sup> \u2212 7<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nf(x) = 4 \u2212 x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 35\" width=\"582\" height=\"321\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-35.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-35-300x165.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 36.<br \/>\nf(x) = 3(x \u2212 10)(x + 4)<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ng(x) = \u2212(x + 2)(x + 8)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 37\" width=\"579\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-37.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-37-300x165.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 38.<br \/>\nh(x) = \\(\\frac{1}{2}\\)(x \u2212 1)<sup>2<\/sup> \u2212 3<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nf(x) = \u22122x<sup>2<\/sup> + 4x \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.7 Question 39\" width=\"599\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-39.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.7-Question-39-300x161.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><\/p>\n<h3><a id=\"Lesson_4.8_Analyzing_Graphs_of_Polynomial_Functions\"><\/a>Lesson 4.8 Analyzing Graphs of Polynomial Functions<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow many turning points can the graph of a polynomial function have?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-92.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 92\" width=\"233\" height=\"185\" \/><br \/>\nA turning point of the graph of a polynomial function is a point on the graph at which the function changes from<\/p>\n<ul>\n<li>increasing to decreasing, or<\/li>\n<li>decreasing to increasing.<\/li>\n<\/ul>\n<p><b>EXPLORATION 1<br \/>\nApproximating Turning Points<br \/>\nWork with a partner.<\/b> Match each polynomial function with its graph. Explain your reasoning. Then use a graphing calculator to approximate the coordinates of the turning points of the graph of the function. Round your answers to the nearest hundredth.<br \/>\na. f(x) = 2x<sup>2<\/sup> + 3x \u2212 4<br \/>\nb. f(x) = x<sup>2<\/sup> + 3x + 2<br \/>\nc. f(x) = x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 x + 1<br \/>\nd. f(x) = \u2212x<sup>3<\/sup> + 5x \u2212 2<br \/>\ne. f(x) = x<sup>4<\/sup> \u2212 3x<sup>2<\/sup> + 2x \u2212 1<br \/>\nf. f(x) = \u22122x<sup>5<\/sup> \u2212 x<sup>2<\/sup> + 5x + 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-93.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 93\" width=\"250\" height=\"217\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-94.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 94\" width=\"529\" height=\"455\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-94.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-94-300x258.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 2.<br \/>\nHow many turning points can the graph of a polynomial function have?<\/p>\n<p>Question 3.<br \/>\nIs it possible to sketch the graph of a cubic polynomial function that has no turning points? Justify your answer.<\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>Graph the function.<\/b><\/p>\n<p>Question 1.<br \/>\nf(x) = \\(\\frac{1}{2}\\)(x + 1)(x \u2212 4)<\/p>\n<p>Question 2.<br \/>\nf(x) = \\(\\frac{1}{4}\\)(x + 2)(x \u2212 1)(x \u2212 3)<\/p>\n<p>Question 3.<br \/>\nFind all real zeros of f(x) = 18x<sup>3<\/sup> + 21x<sup>2<\/sup> \u2212 13x \u2212 6.<\/p>\n<p>Question 4.<br \/>\nGraph f(x) = 0.5x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 x + 2. Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing.<\/p>\n<p><b>Determine whether the function is even, odd, or neither.<\/b><\/p>\n<p>Question 5.<br \/>\nf(x) = \u2212x<sup>2<\/sup> + 5<\/p>\n<p>Question 6.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 5x<sup>3<\/sup><\/p>\n<p>Question 7.<br \/>\nf(x) = 2x<sup>5<\/sup><\/p>\n<h3><a id=\"Analyzing_Graphs_of_Polynomial_Functions_4.8_Exercises\"><\/a>Analyzing Graphs of Polynomial Functions 4.8 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE<\/b> A local maximum or local minimum of a polynomial function occurs at a ______________ point of the graph of the function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 1\" width=\"579\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-1-300x32.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING <\/b>Explain what a local maximum of a function is and how it may be different from the maximum value of the function.<br \/>\nAnswer:<\/p>\n<p><b>ANALYZING RELATIONSHIPS In Exercises 3\u20136, match the function with its graph.<\/b><\/p>\n<p>Question 3.<br \/>\nf(x) = (x \u2212 1)(x \u2212 2)(x + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 3\" width=\"416\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-3.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-3-300x24.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 4.<br \/>\nh(x) = (x + 2)<sup>2<\/sup>(x + 1)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\ng(x) = (x + 1)(x \u2212 1)(x + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 5\" width=\"428\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-5.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-5-300x25.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Question 6.<br \/>\nf(x) = (x \u2212 1)<sup>2<\/sup>(x + 2)<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-95.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 95\" width=\"378\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-95.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-95-300x242.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p><b>In Exercises 7\u201314, graph the function.<\/b><\/p>\n<p>Question 7.<br \/>\nf(x) = (x \u2212 2)<sup>2<\/sup>(x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 7\" width=\"573\" height=\"632\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-7.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-7-272x300.png 272w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 8.<br \/>\nf(x) = (x + 2)<sup>2<\/sup>(x + 4)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nh(x) = (x + 1)<sup>2<\/sup>(x \u2212 1)(x \u2212 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 9\" width=\"589\" height=\"680\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-9.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-9-260x300.png 260w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 10.<br \/>\ng(x) = 4(x + 1)(x + 2)(x \u2212 1)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nh(x) = \\(\\frac{1}{3}\\)(x \u2212 5)(x + 2)(x \u2212 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 11\" width=\"580\" height=\"724\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-11.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-11-240x300.png 240w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 12.<br \/>\ng(x) = \\(\\frac{1}{12}\\)(x + 4)(x + 8)(x \u2212 1)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nh(x) = (x\u2212 3)(x<sup>2<\/sup> + x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 13\" width=\"582\" height=\"702\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-13.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-13-249x300.png 249w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = (x \u2212 4)(2x<sup>2<\/sup> \u2212 2x + 1)<br \/>\nAnswer:<\/p>\n<p><b>ERROR ANALYSIS In Exercises 15 and 16, describe and correct the error in using factors to graph f.<\/b><\/p>\n<p>Question 15.<br \/>\nf(x) = (x + 2)(x \u2212 1)<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-96.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 96\" width=\"307\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-96.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-96-300x181.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 15\" width=\"525\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-15.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-15-300x173.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = x<sup>2<\/sup>(x \u2212 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-97.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 97\" width=\"312\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-97.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-97-300x171.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 17\u201322, find all real zeros of the function.<\/b><\/p>\n<p>Question 17.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> \u2212 x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 17\" width=\"586\" height=\"423\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-17.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-17-300x217.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 18.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> \u2212 4x + 12<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nh(x) = 2x<sup>3<\/sup> + 7x<sup>2<\/sup> \u2212 5x \u2212 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 19\" width=\"602\" height=\"462\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-19.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-19-300x230.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 20.<br \/>\nh(x) = 4x<sup>3<\/sup> \u2212 2x<sup>2<\/sup> \u2212 24x \u2212 18<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ng(x) = 4x<sup>3<\/sup> + x<sup>2<\/sup> \u2212 51x + 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 21\" width=\"608\" height=\"431\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-21.png 608w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-21-300x213.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>Question 22.<br \/>\nf(x) = 2x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> \u2212 32x \u2212 15<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 23\u201330, graph the function. Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing.<\/b><\/p>\n<p>Question 23.<br \/>\ng(x) = 2x<sup>3<\/sup> + 8x<sup>2<\/sup> \u2212 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 23\" width=\"570\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-23.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-23-300x206.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 24.<br \/>\ng(x) = \u2212x<sup>4<\/sup> + 3x<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nh(x) = x<sup>4<\/sup> \u2212 3x<sup>2<\/sup> + x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 25\" width=\"584\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-25.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-25-300x230.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = x<sup>5<\/sup> \u2212 4x<sup>3<\/sup> + x<sup>2<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nf(x) = 0.5x<sup>3<\/sup> \u2212 2x + 2.5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 27\" width=\"579\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-27.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-27-300x203.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 28.<br \/>\nf(x) = 0.7x<sup>4<\/sup> \u2212 3x<sup>3<\/sup> + 5x<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nh(x) = x<sup>5<\/sup> + 2x<sup>2<\/sup> \u2212 17x \u2212 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 29\" width=\"574\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-29.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-29-300x228.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 30.<br \/>\ng(x) = x<sup>4<\/sup> \u2212 5x<sup>3<\/sup> + 2x<sup>2<\/sup> + x \u2212 3<br \/>\nAnswer:<\/p>\n<p><b>In Exercises 31\u201336, estimate the coordinates of each turning point. State whether each corresponds to a local maximum or a local minimum. Then estimate the real zeros and find the least possible degree of the function.<\/b><\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-98.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 98\" width=\"156\" height=\"149\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 31\" width=\"570\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-31.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-31-300x61.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-99.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 99\" width=\"153\" height=\"151\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-100.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 100\" width=\"154\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-100.png 154w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-100-150x150.png 150w\" sizes=\"(max-width: 154px) 100vw, 154px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 33\" width=\"582\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-33.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-33-300x44.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-101.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 101\" width=\"159\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-102.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 102\" width=\"154\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 35\" width=\"565\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-35.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-35-300x47.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-103.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 103\" width=\"157\" height=\"152\" \/><br \/>\nAnswer:<\/p>\n<p><b>OPEN-ENDED In Exercises 37 and 38, sketch a graph of a polynomial function f having the given characteristics.<\/b><\/p>\n<p>Question 37.<\/p>\n<ul>\n<li>The graph of f has x-intercepts at x = \u22124, x = 0, and x = 2.<\/li>\n<li>f has a local maximum value when x = 1.<\/li>\n<li>f has a local minimum value when x = \u22122.<\/li>\n<\/ul>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 37\" width=\"559\" height=\"348\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-37.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-37-300x187.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 38.<\/p>\n<ul>\n<li>The graph of f has x-intercepts at x = \u22123, x = 1, and x = 5.<\/li>\n<li>f has a local maximum value when x = 1.<\/li>\n<li>f has a local minimum value when x = \u22122 and when x = 4.<\/li>\n<\/ul>\n<p>Answer:<\/p>\n<p><b>In Exercises 39\u201346, determine whether the function is even, odd, or neither.<\/b><\/p>\n<p>Question 39.<br \/>\nh(x) = 4x<sup>7<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 39\" width=\"421\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-39.png 421w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-39-300x73.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p>Question 40.<br \/>\ng(x) = \u22122x<sup>6<\/sup> + x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nf(x) = x<sup>4<\/sup> + 3x<sup>2<\/sup> \u2212 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 41\" width=\"497\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-41.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-41-300x63.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>Question 42.<br \/>\nf(x) = x<sup>5<\/sup> + 3x<sup>3<\/sup> \u2212 x<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ng(x) = x<sup>2<\/sup> + 5x + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 43\" width=\"578\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-43.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-43-300x80.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 44.<br \/>\nf(x) = \u2212x<sup>3<\/sup> + 2x \u2212 9<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 12x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 45\" width=\"437\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-45.png 437w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-45-300x69.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><\/p>\n<p>Question 46.<br \/>\nh(x) = x<sup>5<\/sup> + 3x<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<b>USING TOOLS<\/b> When a swimmer does the breaststroke, the function<br \/>\nS = \u2212241t<sup>7<\/sup> + 1060t<sup>6<\/sup> \u2212 1870t<sup>5<\/sup> + 1650t<sup>4<\/sup> \u2212 737t<sup>3<\/sup> + 144t<sup>2<\/sup> \u2212 2.43t<br \/>\nmodels the speed S (in meters per second) of the swimmer during one complete stroke, where t is the number of seconds since the start of the stroke and 0 \u2264 t \u2264 1.22. Use a graphing calculator to graph the function. At what time during the stroke is the swimmer traveling the fastest?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-104.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 104\" width=\"277\" height=\"191\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 47\" width=\"555\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-47.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-47-300x137.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 48.<br \/>\n<b>USING TOOLS <\/b>During a recent period of time, the number S (in thousands) of students enrolled in public schools in a certain country can be modeled by S = 1.64x<sup>3<\/sup> \u2212 102x<sup>2<\/sup> + 1710x + 36,300, where x is time (in years). Use a graphing calculator to graph the function for the interval 0 \u2264 x \u2264 41. Then describe how the public school enrollment changes over this period of time.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<b>WRITING <\/b>Why is the adjective local, used to describe the maximums and minimums of cubic functions, sometimes not required for quadratic functions?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 49\" width=\"536\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-49.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-49-300x35.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 50.<br \/>\n<b>HOW DO YOU SEE IT? <\/b>The graph of a polynomial function is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-105.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 105\" width=\"183\" height=\"176\" \/><br \/>\na. Find the zeros, local maximum, and local minimum values of the function.<br \/>\nb. Compare the x-intercepts of the graphs of y = f(x) and y = \u2212f(x).<br \/>\nc. Compare the maximum and minimum values of the functions y = f(x) and y = \u2212f(x).<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend claims that the product of two odd functions is an odd function. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 51\" width=\"584\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-51.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-51-300x58.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 52.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>You are making a rectangular box out of a 16-inch-by-20-inch piece of cardboard. The box will be formed by making the cuts shown in the diagram and folding up the sides. You want the box to have the greatest volume possible.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-106.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 106\" width=\"220\" height=\"169\" \/><br \/>\na. How long should you make the cuts?<br \/>\nb. What is the maximum volume?<br \/>\nc. What are the dimensions of the finished box?<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<b>PROBLEM SOLVING<\/b> Quonset huts are temporary, all-purpose structures shaped like half-cylinders. You have 1100 square feet of material to build a quonset hut.<br \/>\na. The surface area S of a quonset hut is given by S = \u03c0r<sup>2<\/sup> + \u03c0r\u2113. Substitute 1100 for S and then write an expression for \u2113 in terms of r.<br \/>\nb. The volume V of a quonset hut is given by V = 1 \u2014 2\u03c0r<sup>2<\/sup>\u2113. Write an equation that gives V as a function in terms of r only.c. Find the value of r that maximizes the volume of the hut.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-107.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 107\" width=\"331\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-107.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-107-300x190.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 53\" width=\"576\" height=\"737\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-53.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-53-234x300.png 234w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 54.<br \/>\n<b>THOUGHT PROVOKING<\/b> Write and graph a polynomial function that has one real zero in each of the intervals \u22122 &lt; x &lt; \u22121, 0 &lt; x &lt; 1, and 4 &lt; x &lt; 5. Is there a maximum degree that such a polynomial function can have? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<b>MATHEMATICAL CONNECTIONS<\/b> A cylinder is inscribed in a sphere of radius 8 inches. Write an equation for the volume of the cylinder as a function of h. Find the value of h that maximizes the volume of the inscribed cylinder. What is the maximum volume of the cylinder?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-108.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 108\" width=\"211\" height=\"176\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-55.1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 55.1\" width=\"581\" height=\"537\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-55.1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-55.1-300x277.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-55.2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 55.2\" width=\"591\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-55.2.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-55.2-300x141.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>State whether the table displays linear data, quadratic data, or neither. Explain<\/b><\/p>\n<p>Question 56.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-109.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 109\" width=\"317\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-109.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-109-300x69.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-110.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 110\" width=\"311\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-110.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-110-300x73.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-57.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 4 Polynomial Functions 4.8 a 57\" width=\"562\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-57.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-4-Polynomial-Functions-4.8-a-57-300x82.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<h3><a id=\"Lesson_4.9_Modeling_with_Polynomial_Functions\"><\/a>Lesson 4.9 Modeling with Polynomial Functions<\/h3>\n<p><b>Essential Question<\/b><br \/>\nHow can you find a polynomial model for real-life data?<\/p>\n<p><b>EXPLORATION 1<br \/>\nModeling Real-Life Data<br \/>\nWork with a partner. <\/b>The distance a baseball travels after it is hit depends on the angle at which it was hit and the initial speed. The table shows the distances a baseball hit at an angle of 35\u00b0 travels at various initial speeds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-111.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 111\" width=\"542\" height=\"108\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-111.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-111-300x60.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><br \/>\na. Recall that when data have equally-spaced x-values, you can analyze patterns in the differences of the y-values to determine what type of function can be used to model the data. If the first differences are constant, then the set of data fits a linear model. If the second differences are constant, then the set of data fits a quadratic model.Find the first and second differences of the data. Are the data linear or quadratic? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-112.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 112\" width=\"366\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-112.png 366w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-112-300x102.png 300w\" sizes=\"(max-width: 366px) 100vw, 366px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-113.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 113\" width=\"263\" height=\"215\" \/><br \/>\nb. Use a graphing calculator to draw a scatter plot of the data. Do the data appear linear or quadratic? Use the regression feature of the graphing calculator to find a linear or quadratic model that best fits the data.12019075400<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-113.1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 113.1\" width=\"213\" height=\"148\" \/><br \/>\nc. Use the model you found in part (b) to find the distance a baseball travels when it is hit at an angle of 35\u00b0 and travels at an initial speed of 120 miles per hour.<br \/>\nd. According to the Baseball Almanac, \u201cAny drive over400 feet is noteworthy. A blow of 450 feet shows exceptional power, as the majority of major league players are unable to hit a ball that far. Anything in the 500-foot range is genuinely historic.\u201d Estimate the initial speed of a baseball that travels a distance of 500 feet.<\/p>\n<p><b>Communicate Your Answer<\/b><\/p>\n<p>Question 2.<br \/>\nHow can you find a polynomial model for real-life data?<\/p>\n<p>Question 3.<br \/>\nHow well does the model you found in Exploration 1(b) fit the data? Do you think the model is valid for any initial speed? Explain your reasoning.<\/p>\n<p><b>4.9 Lesson<\/b><\/p>\n<p><b>Monitoring Progress<\/b><\/p>\n<p><b>write a cubic function whose graph passes through the given points.\u00a0<\/b><\/p>\n<p>Question 1.<br \/>\n(\u22124, 0), (0, 10), (2, 0), (5, 0)<\/p>\n<p>Question 2.<br \/>\n(\u22121, 0), (0, \u221212), (2, 0), (3, 0)<\/p>\n<p>Question 3.<br \/>\nUse finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-118.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 118\" width=\"327\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-118.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-118-300x83.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p><b>Use a graphing calculator to find a polynomial function that fits the data.<\/b><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-119.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 119\" width=\"260\" height=\"80\" \/><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-120.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 120\" width=\"257\" height=\"73\" \/><\/p>\n<h3><a id=\"Modeling_with_polynomial_Functions_4.9_Exercises\"><\/a>Modeling with polynomial Functions 4.9 Exercises<\/h3>\n<p><b>Vocabulary and Core Concept Check<\/b><\/p>\n<p>Question 1.<br \/>\n<b>COMPLETE THE SENTENCE <\/b>When the x-values in a set of data are equally spaced, the differences of consecutive y-values are called ________________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 1\" width=\"608\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-1.png 608w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-1-300x30.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>Question 2.<br \/>\n<b>WRITING <\/b>Explain how you know when a set of data could be modeled by a cubic function.<br \/>\nAnswer:<\/p>\n<p><b>Monitoring Progress and Modeling with Mathematics<\/b><\/p>\n<p><b>In Exercises 3\u20136, write a cubic function whose graph is shown.<\/b><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-121.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 121\" width=\"179\" height=\"164\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 3\" width=\"562\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-3.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-3-300x157.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-122.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 122\" width=\"189\" height=\"170\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-123.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 123\" width=\"179\" height=\"181\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 5\" width=\"574\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-5.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-5-300x158.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-124.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 124\" width=\"191\" height=\"179\" \/><br \/>\nAnswer:<\/p>\n<p><b>In Exercises 7\u201312, use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.<\/b><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-125.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 125\" width=\"375\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-125.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-125-300x62.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 7\" width=\"557\" height=\"527\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-7.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-7-300x284.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-126.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 126\" width=\"379\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-126.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-126-300x65.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n(\u22124, \u2212317), (\u22123, \u221237), (\u22122, 21), (\u22121, 7), (0, \u22121), (1, 3), (2, \u221247), (3, \u2212289), (4, \u2212933)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 9\" width=\"574\" height=\"545\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-9.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-9-300x285.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 10.<br \/>\n(\u22126, 744), (\u22124, 154), (\u22122, 4), (0, \u22126), (2, 16), (4, 154), (6, 684), (8, 2074), (10, 4984)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n(\u22122, 968), (\u22121, 422), (0, 142), (1, 26), (2, \u22124), (3, \u22122), (4, 2), (5, 2), (6, 16)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 11\" width=\"572\" height=\"536\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-11.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-11-300x281.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 12.<br \/>\n(1, 0), (2, 6), (3, 2), (4, 6), (5, 12), (6, \u221210), (7, \u2212114), (8, \u2212378), (9, \u2212904)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<b>ERROR ANALYSIS<\/b> Describe and correct the error in writing a cubic function whose graph passes through the given points.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-127.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 127\" width=\"370\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-127.png 370w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-127-300x148.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 13\" width=\"580\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-13.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-13-300x122.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 14.<br \/>\n<b>MODELING WITH MATHEMATICS<\/b> The dot patterns show pentagonal numbers. The number of dots in the nth pentagonal number is given by f(n) = \\(\\frac{1}{2}\\)n(3n \u2212 1). Show that this function has constant second-order differences.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-128.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 128\" width=\"375\" height=\"101\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-128.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-128-300x81.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<b>OPEN-ENDED<\/b> Write three different cubic functions that pass through the points (3, 0), (4, 0), and (2, 6). Justify your answers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 15\" width=\"556\" height=\"375\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-15.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-15-300x202.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 16.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The table shows the ages of cats and their corresponding ages in human years. Find a polynomial model for the data for the first 8 years of a cat\u2019s life. Use the model to estimate the age (in human years) of a cat that is 3 years old.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-129.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 129\" width=\"360\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-129.png 360w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-129-300x60.png 300w\" sizes=\"(max-width: 360px) 100vw, 360px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<b>MODELING WITH MATHEMATICS <\/b>The data in the table show the average speeds y (in miles per hour) of a pontoon boat for several different engine speeds x (in hundreds of revolutions per minute, or RPMs). Find a polynomial model for the data. Estimate the average speed of the pontoon boat when the engine speed is 2800 RPMs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-130.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 130\" width=\"325\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-130.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-130-300x79.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 17\" width=\"577\" height=\"646\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-17.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-17-268x300.png 268w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 18.<br \/>\nHOW DO YOU SEE IT? The graph shows typical speeds y (in feet per second) of a space shuttle x seconds after it is launched.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-131.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 131\" width=\"307\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-131.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-131-300x197.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\na. What type of polynomial function models the data? Explain.<br \/>\nb. Which nth-order finite difference should be constant for the function in part (a)? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<b>MATHEMATICAL CONNECTIONS <\/b>The table shows the number of diagonals for polygons with n sides. Find a polynomial function that fits the data. Determine the total number of diagonals in the decagon shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-132.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 132\" width=\"119\" height=\"107\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-133.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 133\" width=\"357\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-133.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-133-300x97.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 19\" width=\"565\" height=\"618\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-19.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-19-274x300.png 274w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 20.<br \/>\n<b>MAKING AN ARGUMENT<\/b> Your friend states that it is not possible to determine the degree of a function given the first-order differences. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<b>WRITING <\/b>Explain why you cannot always use finite differences to find a model for real-life data sets.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 21\" width=\"562\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-21.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-21-300x30.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 22.<br \/>\n<b>THOUGHT PROVOKING<\/b> A, B, and C are zeros of a cubic polynomial function. Choose values for A, B, and C such that the distance from A to B is less than or equal to the distance from A to C. Then write the function using the A, B, and C values you chose.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<b>MULTIPLE REPRESENTATIONS<\/b> Order the polynomial functions according to their degree, from least to greatest.<br \/>\nA.f(x) = \u22123x + 2x<sup>2<\/sup> + 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-134.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 134\" width=\"369\" height=\"356\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-134.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-134-300x289.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 23\" width=\"604\" height=\"553\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-23.png 604w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-23-300x275.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p>Question 24.<br \/>\n<b>ABSTRACT REASONING<\/b> Substitute the expressions z, z + 1, z + 2, &#8230;&#8230;.. , z + 5 for x in the function f(x) = ax<sup>3<\/sup> + bx<sup>2<\/sup> + cx + d to generate six equally-spaced ordered pairs. Then show that the third-order differences are constant.<br \/>\nAnswer:<\/p>\n<p><b>Maintaining Mathematical Proficiency<\/b><\/p>\n<p><b>Solve the equation using square roots<\/b>.(Section 3.1)<\/p>\n<p>Question 25.<br \/>\nx<sup>2<\/sup> \u2212 6 = 30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 25\" width=\"386\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-25.png 386w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-25-300x131.png 300w\" sizes=\"(max-width: 386px) 100vw, 386px\" \/><\/p>\n<p>Question 26.<br \/>\n5x<sup>2<\/sup> \u2212 38 = 187<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n2(x \u2212 3)<sup>2<\/sup> = 24<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 27\" width=\"505\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-27.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-27-300x100.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\frac{4}{3}\\)(x + 5)<sup>2<\/sup> = 4<br \/>\nAnswer:<\/p>\n<p><b>Solve the equation using the Quadratic Formula.<\/b>(Section 3.4)<\/p>\n<p>Question 29.<br \/>\n2x<sup>2<\/sup> + 3x = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 29\" width=\"426\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-29.png 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-29-300x207.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><\/p>\n<p>Question 30.<br \/>\n2x<sup>2<\/sup> + \\(\\frac{1}{2}\\) = 2x<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n2x<sup>2<\/sup> + 3x =\u22123x<sup>2<\/sup> + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-47845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions 4.9 a 31\" width=\"545\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-31.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-4-Polynomial-Functions-4.9-a-31-300x142.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 32.<br \/>\n4x \u2212 20 = x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<h3><a id=\"Polynomial_Functions_Performance_Task\"><\/a>Polynomial Functions Performance Task: For the Birds-Wildlife Management<\/h3>\n<p><b>Core Vocabulary<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-135.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 135\" width=\"683\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-135.png 683w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-135-300x37.png 300w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/p>\n<p><b>Core Concepts<\/b><br \/>\n<b>Section 4.5<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-136.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 4 Polynomial Functions 136\" width=\"672\" height=\"28\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-136.png 672w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-136-300x13.png 300w\" sizes=\"(max-width: 672px) 100vw, 672px\" \/><\/p>\n<p><b>Section 4.6<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-137.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 4 Polynomial Functions 137\" width=\"622\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-137.png 622w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-137-300x25.png 300w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/p>\n<p><b>Section 4.7<\/b><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-40110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-138.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 4 Polynomial Functions 138\" width=\"727\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-138.png 727w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-138-300x14.png 300w\" sizes=\"(max-width: 727px) 100vw, 727px\" \/><\/p>\n<p><b>Section 4.8<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-139.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 4 Polynomial Functions 139\" width=\"706\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-139.png 706w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-139-300x24.png 300w\" sizes=\"(max-width: 706px) 100vw, 706px\" \/><\/p>\n<p><b>Section 4.9<\/b><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-140.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 4 Polynomial Functions 140\" width=\"645\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-140.png 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-4-Polynomial-Functions-140-300x17.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><\/p>\n<p><b>Mathematical Practices<\/b><\/p>\n<p>Question 1.<br \/>\nExplain how understanding the Complex Conjugates Theorem allows you to construct your argument in Exercise 46 on page 203.<\/p>\n<p>Question 2.<br \/>\nDescribe how you use structure to accurately match each graph with its transformation in Exercises 7\u201310 on page 209.<\/p>\n<p><b>Performance Task<\/b><br \/>\n<b>For the Birds -Wildlife Management<\/b><br \/>\nHow does the presence of humans affect the population of sparrows in a park? Do more humans mean fewer sparrows? Or does the presence of humans increase the number of sparrows up to a point? Are there a minimum number of sparrows that can be found in a park, regardless of how many humans there are? What can a mathematical model tell you?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-204.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 204\" width=\"422\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-204.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-204-300x213.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><br \/>\nTo explore the answers to these questions and more, go to BigIdeasMath.com.<\/p>\n<h3><a id=\"Polynomial_Functions_Chapter_Review\"><\/a>Polynomial Functions Chapter Review<\/h3>\n<p><b>Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.<\/b><\/p>\n<p>Question 1.<br \/>\nh(x) = \u2212x<sup>3<\/sup> + 2x<sup>2<\/sup> \u2212 15x<sup>7<\/sup><\/p>\n<p>Question 2.<br \/>\np(x) = x<sup>3<\/sup> \u2212 5x<sup>0.5<\/sup> + 13x<sup>2<\/sup> + 8<\/p>\n<p><b>Graph the polynomial function.<\/b><\/p>\n<p>Question 3.<br \/>\nh(x) = x<sup>2<\/sup> + 6x<sup>5<\/sup> \u2212 5<\/p>\n<p>Question 4.<br \/>\nf(x) = 3x<sup>4<\/sup> \u2212 5x<sup>2<\/sup> + 1<\/p>\n<p>Question 5.<br \/>\ng(x) = \u2212x<sup>4<\/sup> + x + 2<\/p>\n<p><b>Find the sum or difference.<\/b><\/p>\n<p>Question 6.<br \/>\n(4x<sup>3<\/sup> \u2212 12x<sup>2<\/sup> \u2212 5) \u2212 (\u22128x<sup>2<\/sup> + 4x + 3)<\/p>\n<p>Question 7.<br \/>\n(x<sup>4<\/sup> + 3x<sup>3<\/sup> \u2212 x<sup>2<\/sup> + 6) + (2x<sup>4<\/sup> \u2212 3x + 9)<\/p>\n<p>Question 8.<br \/>\n(3x<sup>2<\/sup> + 9x + 13) \u2212 (x<sup>2<\/sup> \u2212 2x + 12)<\/p>\n<p><b>Find the product.<\/b><\/p>\n<p>Question 9.<br \/>\n(2y<sup>2<\/sup> + 4y \u2212 7)(y + 3)<\/p>\n<p>Question 10.<br \/>\n(2m + n)<sup>3<\/sup><\/p>\n<p>Question 11.<br \/>\n(s + 2)(s + 4)(s \u2212 3)<\/p>\n<p><b>Use Pascal\u2019s Triangle to expand the binomial.<\/b><\/p>\n<p>Question 12.<br \/>\n(m + 4)<sup>4<\/sup><\/p>\n<p>Question 13.<br \/>\n(3s + 2)<sup>5<\/sup><\/p>\n<p>Question 14.<br \/>\n(z + 1)<sup>6<\/sup><\/p>\n<p><b>Divide using polynomial long division or synthetic division.<\/b><\/p>\n<p>Question 15.<br \/>\n(x<sup>3<\/sup> + x<sup>2<\/sup> + 3x \u2212 4) \u00f7 (x<sup>2<\/sup> + 2x + 1)<\/p>\n<p>Question 16.<br \/>\n(x<sup>4<\/sup> + 3x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> + 5x + 3) \u00f7 (x<sup>2<\/sup> + x + 4)<\/p>\n<p>Question 17.<br \/>\n(x<sup>4<\/sup> \u2212 x<sup>2<\/sup> \u2212 7) \u00f7 (x + 4)<\/p>\n<p>Question 18.<br \/>\nUse synthetic division to evaluate g(x) = 4x<sup>3<\/sup> + 2x<sup>2<\/sup> \u2212 4 when x = 5.<\/p>\n<p><b>Factor the polynomial completely.<\/b><\/p>\n<p>Question 19.<br \/>\n64x<sup>3<\/sup> \u2212 8<\/p>\n<p>Question 20.<br \/>\n2z<sup>5<\/sup> \u2212 12z<sup>3<\/sup> + 10z<\/p>\n<p>Question 21.<br \/>\n2a<sup>3<\/sup> \u2212 7a<sup>2<\/sup> \u2212 8a + 28<\/p>\n<p>Question 22.<br \/>\nShow that x + 2 is a factor of f(x) = x<sup>4<\/sup> + 2x<sup>3<\/sup> \u2212 27x \u2212 54. Then factor f(x) completely.<\/p>\n<p><b>Find all real solutions of the equation.<\/b><\/p>\n<p>Question 23.<br \/>\nx<sup>3<\/sup> + 3x<sup>2<\/sup> \u2212 10x \u2212 24 = 0<\/p>\n<p>Question 24.<br \/>\nx<sup>3<\/sup> + 5x<sup>2<\/sup> \u2212 2x \u2212 24 = 0<\/p>\n<p><b>Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.<\/b><\/p>\n<p>Question 25.<br \/>\n1, 2 \u2212 \\(\\sqrt{3}\\)<\/p>\n<p>Question 26.<br \/>\n2, 3, \\(\\sqrt{5}\\)<\/p>\n<p>Question 27.<br \/>\n\u22122, 5, 3 + \\(\\sqrt{6}\\)<\/p>\n<p>Question 28.<br \/>\nYou use 240 cubic inches of clay to make a sculpture shaped as a rectangular prism. The width is 4 inches less than the length and the height is 2 inches more than three times the length. What are the dimensions of the sculpture? Justify your answer.<\/p>\n<p><b>Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.<\/b><\/p>\n<p>Question 29.<br \/>\n3, 1 + 2i<\/p>\n<p>Question 30.<br \/>\n\u22121, 2, 4i<\/p>\n<p>Question 31.<br \/>\n\u22125, \u22124, 1 \u2212i\\(\\sqrt{3}\\)<\/p>\n<p><b>Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function.<\/b><\/p>\n<p>Question 32.<br \/>\nf(x) = x<sup>4<\/sup> \u2212 10x + 8<\/p>\n<p>Question 33.<br \/>\nf(x) = \u22126x<sup>4<\/sup> \u2212 x<sup>3<\/sup> + 3x<sup>2<\/sup> + 2x + 18<\/p>\n<p><b>Describe the transformation of f represented by g. Then graph each function.<\/b><\/p>\n<p>Question 34.<br \/>\nf(x) = x<sup>3<\/sup>, g(x) = (\u2212x)<sup>3<\/sup> + 2<\/p>\n<p>Question 35.<br \/>\nf(x) = x<sup>4<\/sup>, g(x) = \u2212(x + 9)<sup>4<\/sup><\/p>\n<p><b>Write a rule for g.<\/b><\/p>\n<p>Question 36.<br \/>\nLet the graph of g be a horizontal stretch by a factor of 4, followed by a translation 3 units right and 5 units down of the graph of f(x) = x<sup>5<\/sup> + 3x.<\/p>\n<p>Question 37.<br \/>\nLet the graph of g be a translation 5 units up, followed by a reflection in the y-axis of the graph of f(x) = x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> \u2212 12.<\/p>\n<p><b>Graph the function. Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing.<\/b><\/p>\n<p>Question 38.<br \/>\nf(x) = \u22122x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> \u2212 1<\/p>\n<p>Question 39.<br \/>\nf(x) = x<sup>4<\/sup> + 3x<sup>3<\/sup> \u2212 x<sup>2<\/sup> \u2212 8x + 2<\/p>\n<p><b>Determine whether the function is even, odd, or neither.<\/b><\/p>\n<p>Question 40.<br \/>\nf(x) = 2x<sup>3<\/sup> + 3x<\/p>\n<p>Question 41.<br \/>\ng(x) = 3x<sup>2<\/sup> \u2212 7<\/p>\n<p>Question 42.<br \/>\nh(x) = x<sup>6<\/sup> + 3x<sup>5<\/sup><\/p>\n<p>Question 43.<br \/>\nWrite a cubic function whose graph passes through the points (\u22124, 0), (4, 0), (0, 6), and (2, 0).<\/p>\n<p>Question 44.<br \/>\nUse finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-206.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 206\" width=\"314\" height=\"82\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-206.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-206-300x78.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<h3><a id=\"Polynomial_Functions_Chapter_Test\"><\/a>Polynomial Functions Chapter Test<\/h3>\n<p><b>Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.<\/b><\/p>\n<p>Question 1.<br \/>\n3, 1 \u2212 \\(\\sqrt{2}\\)<\/p>\n<p>Question 2.<br \/>\n\u22122, 4, 3i<\/p>\n<p><b>Find the product or quotient.<\/b><\/p>\n<p>Question 3.<br \/>\n(x<sup>6<\/sup> \u2212 4)(x<sup>2<\/sup> \u2212 7x + 5)<\/p>\n<p>Question 4.<br \/>\n(3x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> \u2212 x \u2212 1) \u00f7 (x<sup>2<\/sup> \u2212 2x + 1)<\/p>\n<p>Question 5.<br \/>\n(2x<sup>3<\/sup> \u2212 3x<sup>2<\/sup> + 5x \u2212 1) \u00f7 (x + 2)<\/p>\n<p>Question 6.<br \/>\n(2x + 3)<sup>3<\/sup><\/p>\n<p>Question 7.<br \/>\nThe graphs of f(x) = x<sup>4<\/sup> and g(x) = (x \u2212 3)<sup>4<\/sup> are shown.<br \/>\na. How many zeros does each function have? Explain.<br \/>\nb. Describe the transformation of f represented by g.<br \/>\nc. Determine the intervals for which the function g is increasing or decreasing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-207.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 207\" width=\"203\" height=\"176\" \/><\/p>\n<p>Question 8.<br \/>\nThe volume V (in cubic feet) of an aquarium is modeled by the polynomial function V(x) = x<sup>3<\/sup> + 2x<sup>2<\/sup> \u2212 13x + 10, where x is the length of the tank.<br \/>\na. Explain how you know x = 4 is not a possible rational zero.<br \/>\nb. Show that x \u2212 1 is a factor of V(x). Then factor V(x) completely.<br \/>\nc. Find the dimensions of the aquarium shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-208.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 208\" width=\"260\" height=\"220\" \/><\/p>\n<p>Question 9.<br \/>\nOne special product pattern is (a \u2212 b)<sup>2<\/sup> = a<sup>2<\/sup> \u2212 2ab + b<sup>2<\/sup>. Using Pascal\u2019s Triangle to expand (a \u2212 b)<sup>2<\/sup> gives 1a<sup>2<\/sup> + 2a(\u2212b) + 1(\u2212b)<sup>2<\/sup>. Are the two expressions equivalent? Explain.<\/p>\n<p>Question 10.<br \/>\nCan you use the synthetic division procedure that you learned in this chapter to divide any two polynomials? Explain.<\/p>\n<p>Question 11.<br \/>\nLet T be the number (in thousands) of new truck sales. Let C be the number (in thousands) of new car sales. During a 10-year period, T and C can be modeled by the following equations where t is time (in years).<br \/>\nT = 23t<sup>4<\/sup> \u2212 330t<sup>3<\/sup> + 3500t<sup>2<\/sup> \u2212 7500t + 9000<br \/>\nC = 14t<sup>4<\/sup> \u2212 330t<sup>3<\/sup> + 2400t<sup>2<\/sup> \u2212 5900t + 8900<br \/>\na. Find a new model S for the total number of new vehicle sales.<br \/>\nb. Is the function S even, odd, or neither? Explain your reasoning.<\/p>\n<p>Question 12.<br \/>\nYour friend has started a golf caddy business. The table shows the profits p (in dollars) of the business in the first 5 months. Use finite differences to find a polynomial model for the data. Then use the model to predict the profit after 7 months.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-209.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 209\" width=\"344\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-209.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-209-300x65.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><\/p>\n<h3><a id=\"Polynomial_Functions_Cumulative_Assessment\"><\/a>Polynomial Functions Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nThe synthetic division below represents f(x) \u00f7 (x\u2212 3). Choose a value for m so that x \u2212 3 is a factor of f(x). Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-210.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 210\" width=\"379\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-210.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-210-300x123.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p>Question 2.<br \/>\nAnalyze the graph of the polynomial function to determine the sign of the leading coefficient, the degree of the function, and the number of real zeros. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-211.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 211\" width=\"227\" height=\"220\" \/><\/p>\n<p>Question 3.<br \/>\nWhich statement about the graph of the equation 12(x\u2212 6) = \u2212( y + 4)<sup>2<\/sup> is not true?<br \/>\nA. The vertex is (6, \u22124).<br \/>\nB. The axis of symmetry is y = \u22124.<br \/>\nC. The focus is (3, \u22124).<br \/>\nD. The graph represents a function.<\/p>\n<p>Question 4.<br \/>\nA parabola passes through the point shown in the graph. The equation of the axis of symmetry is x = \u2212a. Which of the given points could lie on the parabola? If the axis of symmetry was x = a, then which points could lie on the parabola? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-212.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 212\" width=\"513\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-212.png 513w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-212-300x129.png 300w\" sizes=\"(max-width: 513px) 100vw, 513px\" \/><\/p>\n<p>Question 5.<br \/>\nSelect values for the function to model each transformation of the graph of f(x) = x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-213.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 213\" width=\"221\" height=\"54\" \/><br \/>\na. The graph is a translation 2 units up and 3 units left.<br \/>\nb. The graph is a translation 2 units right and 3 units down.<br \/>\nc. The graph is a vertical stretch by a factor of 2, followed by a translation 2 units up.<br \/>\nd. The graph is a translation 3 units right and a vertical shrink by a factor of \\(\\frac{1}{2}\\), followed by a translation 4 units down.<\/p>\n<p>Question 6.<br \/>\nThe diagram shows a circle inscribed in a square. The area of the shaded region is21.5 square meters. To the nearest tenth of a meter, how long is each side of the square?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-214.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 214\" width=\"153\" height=\"156\" \/><br \/>\nA. 4.6 meters<br \/>\nB. 8.7 meters<br \/>\nC. 9.7 meters<br \/>\nD. 10.0 meters<\/p>\n<p>Question 7.<br \/>\nClassify each function as even, odd, or neither. Justify your answer.<br \/>\na. f(x) = 3x<sup>5<\/sup><br \/>\nb. f(x) = 4x<sup>3<\/sup> + 8x<br \/>\nc. f(x) = 3x<sup>5<\/sup> + 12x<sup>2<\/sup>+ 1<br \/>\nd. f(x) = 2x<sup>4<\/sup><br \/>\ne. f(x) = x<sup>11<\/sup> \u2212 x<sup>7<\/sup><br \/>\nf. f(x) = 2x<sup>8<\/sup> + 4x<sup>4<\/sup> + x<sup>2<\/sup> \u2212 5<\/p>\n<p>Question 8.<br \/>\nThe volume of the rectangular prism shown is given by V = 2x<sup>3<\/sup> + 7x<sup>2<\/sup> \u2212 18x \u2212 63. Which polynomial represents the area of the base of the prism?<br \/>\nA. 2x<sup>2<\/sup> + x \u2212 21<br \/>\nB. 2x<sup>2<\/sup> + 21 \u2212 x<br \/>\nC. 13x + 21 + 2x<sup>2<\/sup><br \/>\nD. 2x<sup>2<\/sup> \u2212 21 \u2212 13x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-4-Polynomial-Functions-215.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 4 Polynomial Functions 215\" width=\"268\" height=\"163\" \/><\/p>\n<p>Question 9.<br \/>\nThe number R (in tens of thousands) of retirees receiving Social Security benefits is represented by the function R = 0.286t<sup>3<\/sup> \u2212 4.68t<sup>2<\/sup> + 8.8t + 403, 0 \u2264 t \u2264 10<br \/>\nwhere t represents the number of years since 2000. Identify any turning points on the given interval. What does a turning point represent in this situation?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Algebra 2 Answers Chapter 4 Polynomial Functions are aligned based on the latest syllabus and common core curriculum guidelines. Also, you can get a step-by-step explanation by the subject experts for all questions covered in the Big Ideas Math Book Algebra 2 Ch 4 Polynomials Functions Solution Key. 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