Slide 4 - 1 Copyright © 2009 Pearson Education, Inc. MAT 171 Chapter 4 Review The following is a...

1Copyright © 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

2Copyright © 2009 Pearson Education, Inc.

Active Learning Lecture SlidesFor use with Classroom Response Systems

© 2009 Pearson Education, Inc.

Chapter 4

Copyright © 2009 Pearson Education, Inc. Slide 4 - 3

Chapter 4: Polynomial and

Rational Functions4.1 Polynomial Functions and Models

4.2 Graphing Polynomial Functions

4.3 Polynomial Division; The Remainder and Factor Theorems

4.4 Theorems about Zeros of Polynomial Functions

4.5 Rational Functions

4.6 Polynomial and Rational Inequalities


1. Classify the polynomialP(x) = 5 + 2x2 + 6x4

a. quadratic

c. linear

b. quartic

d. cubic


2. Determine the leading coefficient of the polynomial P(x) = 8x – 9x2 + 7 – x3.

a. 8

c. 1

b. 3

d. 5


3. Determine the degree of the polynomial function P(x) = 5x3 – 6x2 + 2x + 6.

a. 3

c. 5

b. 4

d. 6


4. Which graph represents the polynomial function f(x) = x3 – 3x2 – x + 3?

a. b.

c. d.


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


a. between 1 and 0

c. between 1 and 2

b. between 0 and 1

d. between 2 and 3

6. For f(x) = 2x4 + 3, use the intermediate value theorem to determine which interval contains a zero of f.


a. between 2 and 1

c. between 0 and 1

b. between 1 and 0

d. between 2 and 3

7. For f(x) = 2x4 + 3x + 1, use the intermediate value theorem to determine which interval contains a zero of f.


8. Which graph represents the polynomial function f(x) = x3 – x2 – 4x + 4?

a. b.

c. d.


9. Which graph represents the polynomial function f(x) = x4 – x2 – 4x + 4?

a. b.

c. d.


10. Which graph represents the polynomial function f(x) = –2x2 – 4x?

a. b.

c. d.


a.

c.

b.

d.

11. Use long division to find the quotient and remainder when x4 + 5x2 – 3x + 2 is divided by x – 2.

3 22 9 15, R 32x x x

3 22 9 21, R 44x x x

3 22 9 21, R 44x x x

3 27 14 25, R 52x x x


a.

c.

b.

d.

12. Use synthetic division to find the quotient and remainder when 3x3 – 6x2 + 4 is divided by x + 3.

23 15 45, R 131x x

3 15, R 49x

23 3 9, R 29x x

23 3 9, R 31x x


a. 2

c. 4

b. 8

d. 5

13. Use synthetic division to determine which number is a zero of P(x) = x3 – x2 – 22x + 40.


a. 1276

c. 174

b. 1324

d. 1326

14. Use synthetic division to find P(5) for P(x) = 2x4 – 2x2 + 5x – 1.


a. 5

c. 2

b. 1

d. 10

15. Use synthetic division to find determine which number is a zero of P(x) = x3 – 6x2 + 3x + 10.


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.

2,

2


a.

c.

b.

d.

17. Find a polynomial function of lowest degree with rational coefficients and 3 and 4i as some of its zeros.

2( ) 3 4 12f x x x xi i

3 2( ) 3 16 48f x x x x

3 2( ) 3 16 48f x x x x

3 2( ) 3 16 48f x x x x


a.

c. 5

b. 2

d.

18. Use the rational zeros theorem to determine which number cannot be a zero of P(x) = 10x4 + 6x2 – 5x + 2.

1

5

2

5


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 indicateg(x) = x5 + 4x4 – 2x3 + 3x2 – 6 has?


a.

c.

b.

d. 3

20. Use the rational zeros theorem to determine which number cannot be a zero ofP(x) = 4x4 + 3x2 + x – 3.

4

3

3

4

1

4


a. y = 0

c. x = 4

b. x = 4

d.

21. Find the vertical asymptote for

3

8x

f (x) 6

(x 4)2 .


22. Which graph represents the polynomial

a. b.

c. d.

f (x) x 3

x2 3x 4.function


23. Which graph represents the polynomial

a. b.

c. d.

f (x) 6

(x 2)2 .function


a.

c.

b.

d.

24. Solve (x + 4)(x – 2)(x – 6) ≤ 0.

( 4,2) (6, )

[ 4,2] [6, ]

( , 4) (2,6)

( , 4] [2,6)


a.

c.

b.

d.

25. Solve 3x2 < 17x – 10.

2, (5, )3

2,5

3

2,5

3

3,5

2


a.

c.

b.

d.

26. Solve

17, 5

2

23.

5

x

x

17,

2

17, 5,

2

17, 5

2


a.

c.

b.

d.

27. Solve 3x2 > x + 10.

5, (2, )

3

52,

3

3, 2 ,

5

5, 2 ,

3


a.

c.

b.

d.

28. Solve

31,

5

16.

5

x

x

315,

5

31, 5 ,

5

315,

5


You should work all of the problems before

checking your answers on the next slide.


Answers:

1a 2c 3a 4b5a 6c 7b 8b9c 10a 11a 12a

13d 14d 15c 16a17d 18c 19a 20a21b 22d 23b 24d25c 26a 27d 28b

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