1. Slide 4 - 1 Copyright © 2009 Pearson Education, Inc. MAT 171 Chapter 4 Review The following is a brief review of Chapter 4 for Test 3 that covers Chapters 4 & 5. This does NOT cover all the material that may be on the test. Click on Slide Show and View Slide Show. Read and note your answer to the question. Advance the slide to see the answer. NOTE: Individual slides do NOT contain answers. Work all problems before searching for answers. Dr. Claude Moore, Math Instructor, CFCC

2. Slide 4 - 2 Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. Chapter 4

3. Slide 4 - 3 Copyright © 2009 Pearson Education, Inc. Chapter 4: Polynomial and Rational Functions 4.1Polynomial Functions and Models 4.2Graphing Polynomial Functions 4.3Polynomial Division; The Remainder and Factor Theorems 4.4Theorems about Zeros of Polynomial Functions 4.5Rational Functions 4.6Polynomial and Rational Inequalities

4. Slide 4 - 4 Copyright © 2009 Pearson Education, Inc. 1. Classify the polynomial P(x) = 5 + 2x 2 + 6x 4 a. quadratic c. linear b. quartic d. cubic

5. Slide 4 - 5 Copyright © 2009 Pearson Education, Inc. 2. Determine the leading coefficient of the polynomial P(x) = 8x – 9x 2 + 7 – x 3. a. 8 c.  1 b. 3 d. 5

6. Slide 4 - 6 Copyright © 2009 Pearson Education, Inc. 3. Determine the degree of the polynomial function P(x) = 5x 3 – 6x 2 + 2x + 6. a. 3 c. 5 b. 4 d. 6

7. Slide 4 - 7 Copyright © 2009 Pearson Education, Inc. 4. Which graph represents the polynomial function f(x) = x 3 – 3x 2 – x + 3? a.b. c.d.

8. Slide 4 - 8 Copyright © 2009 Pearson Education, Inc. 5. Find the zeros of the polynomial function and state the multiplicity of each. f(x) = (x + 3) 2 (x + 1) a. –3, multiplicity 2,  1 multiplicity 1 c. –3, multiplicity 2,  1 multiplicity 2 b. 3, multiplicity 2,  1 multiplicity 1 d. 3, multiplicity 3,  1 multiplicity 1

9. Slide 4 - 9 Copyright © 2009 Pearson Education, Inc. a. between  1 and 0 c. between 1 and 2 b. between 0 and 1 d. between 2 and 3 6. For f(x) =  2x 4 + 3, use the intermediate value theorem to determine which interval contains a zero of f.

10. Slide 4 - 10 Copyright © 2009 Pearson Education, Inc. a. between  2 and  1 c. between 0 and 1 b. between  1 and 0 d. between 2 and 3 7. For f(x) =  2x 4 + 3x + 1, use the intermediate value theorem to determine which interval contains a zero of f.

11. Slide 4 - 11 Copyright © 2009 Pearson Education, Inc. 8. Which graph represents the polynomial function f(x) = x 3 – x 2 – 4x + 4? a.b. c.d.

12. Slide 4 - 12 Copyright © 2009 Pearson Education, Inc. 9. Which graph represents the polynomial function f(x) = x 4 – x 2 – 4x + 4? a.b. c.d.

13. Slide 4 - 13 Copyright © 2009 Pearson Education, Inc. 10. Which graph represents the polynomial function f(x) = –2x 2 – 4x? a.b. c.d.

14. Slide 4 - 14 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 11. Use long division to find the quotient and remainder when x 4 + 5x 2 – 3x + 2 is divided by x – 2.

15. Slide 4 - 15 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 12. Use synthetic division to find the quotient and remainder when 3x 3 – 6x 2 + 4 is divided by x + 3.

16. Slide 4 - 16 Copyright © 2009 Pearson Education, Inc. a.  2 c.  4 b. 8 d.  5 13. Use synthetic division to determine which number is a zero of P(x) = x 3 – x 2 – 22x + 40.

17. Slide 4 - 17 Copyright © 2009 Pearson Education, Inc. a.  1276 c. 174 b. 1324 d.  1326 14. Use synthetic division to find P(  5) for P(x) =  2x 4 – 2x 2 + 5x – 1.

18. Slide 4 - 18 Copyright © 2009 Pearson Education, Inc. a.  5 c. 2 b. 1 d.  10 15. Use synthetic division to find determine which number is a zero of P(x) = x 3 – 6x 2 + 3x + 10.

19. Slide 4 - 19 Copyright © 2009 Pearson Education, Inc. a. c.  3 + 2i b.  4 d.  3  2i 16. Suppose that a polynomial function of degree 5 with rational coefficients 4, and 3 – 2i as zeros. Find one other zero.

20. Slide 4 - 20 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 17. Find a polynomial function of lowest degree with rational coefficients and  3 and 4i as some of its zeros.

21. Slide 4 - 21 Copyright © 2009 Pearson Education, Inc. a. c.  5 b.  2 d. 18. Use the rational zeros theorem to determine which number cannot be a zero of P(x) = 10x 4 + 6x 2 – 5x + 2.

22. Slide 4 - 22 Copyright © 2009 Pearson Education, Inc. a. 1 c. 5, 3 or 1 b. 3 or 1 d. 2 or 0 19. How many negative real zeros does Descartes’ rule of signs indicate g(x) =  x 5 + 4x 4 – 2x 3 + 3x 2 – 6 has?

23. Slide 4 - 23 Copyright © 2009 Pearson Education, Inc. a. c. b. d.  3 20. Use the rational zeros theorem to determine which number cannot be a zero of P(x) = 4x 4 + 3x 2 + x – 3.

24. Slide 4 - 24 Copyright © 2009 Pearson Education, Inc. a. y = 0 c. x =  4 b. x = 4 d. 21. Find the vertical asymptote for

25. Slide 4 - 25 Copyright © 2009 Pearson Education, Inc. 22. Which graph represents the polynomial a.b. c.d. function

26. Slide 4 - 26 Copyright © 2009 Pearson Education, Inc. 23. Which graph represents the polynomial a.b. c.d. function

27. Slide 4 - 27 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 24. Solve (x + 4)(x – 2)(x – 6) ≤ 0.

28. Slide 4 - 28 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 25. Solve 3x 2 < 17x – 10.

29. Slide 4 - 29 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 26. Solve

30. Slide 4 - 30 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 27. Solve 3x 2 >  x + 10.

31. Slide 4 - 31 Copyright © 2009 Pearson Education, Inc. a. c. b. d. 28. Solve

32. Slide 4 - 32 Copyright © 2009 Pearson Education, Inc. You should work all of the problems before checking your answers on the next slide.

33. Slide 4 - 33 Copyright © 2009 Pearson Education, Inc. Answers: 1a2c3a4b 5a6c7b8b 9c10a11a12a 13d14d15c16a 17d18c19a20a 21b22d23b24d 25c26a27d28b