Transcript ReviewChapter4
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.
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Dr. Claude Moore, Math Instructor, CFCC
Slide 4 - 1
Copyright © 2009 Pearson Education, Inc.
Active Learning Lecture Slides
For use with Classroom Response Systems
Chapter 4
© 2009 Pearson Education, Inc.
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 2
Chapter 4: Polynomial and Rational Functions
4.1 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
Slide 4 - 3
Copyright © 2009 Pearson Education, Inc.
1. Classify the polynomial
P
(
x
) = 5 + 2
x
2 + 6
x
4 a. quadratic b. quartic c. linear d. cubic Copyright © 2009 Pearson Education, Inc.
Slide 4 - 4
2. Determine the leading coefficient of the polynomial
P
(
x
) = 8
x
– 9
x
2 + 7 –
x
3 .
a. 8 b. 3 c. 1 d. 5 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 5
3. Determine the degree of the polynomial function
P
(
x
) = 5
x
3 – 6
x
2 + 2
x
+ 6.
a. 3 b. 4 c. 5 d. 6 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 6
c.
a.
4. Which graph represents the polynomial function
f
(
x
) =
x
3 – 3
x
2 –
x
+ 3?
b.
d.
Slide 4 - 7
Copyright © 2009 Pearson Education, Inc.
5. Find the zeros of the polynomial function
f
and state the multiplicity of each. (
x
) = (
x
+ 3) 2 (
x
+ 1) a. –3, multiplicity 2, 1 multiplicity 1 b. 3, multiplicity 2, 1 multiplicity 1 c. –3, multiplicity 2, 1 multiplicity 2 d. 3, multiplicity 3, 1 multiplicity 1
Slide 4 - 8
Copyright © 2009 Pearson Education, Inc.
6. For
f
(
x
) = 2
x
4 + 3, use the intermediate value theorem to determine which interval contains a zero of
f
. a. between 1 and 0 b. between 0 and 1 c. between 1 and 2 d. between 2 and 3 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 9
7. For
f
(
x
) = 2
x
4 + 3
x +
1, use the intermediate value theorem to determine which interval contains a zero of
f
. a. between 2 and 1 b. between 1 and 0 c. between 0 and 1 d. between 2 and 3 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 10
c.
a.
8. Which graph represents the polynomial function
f
(
x
) =
x
3 –
x
2 – 4
x
+ 4?
b.
d.
Slide 4 - 11
Copyright © 2009 Pearson Education, Inc.
c.
a.
9. Which graph represents the polynomial function
f
(
x
) =
x
4 –
x
2 – 4
x
+ 4?
b.
d.
Slide 4 - 12
Copyright © 2009 Pearson Education, Inc.
c.
a.
10. Which graph represents the polynomial function
f
(
x
) = –2
x
2 – 4
x
?
b.
d.
Slide 4 - 13
Copyright © 2009 Pearson Education, Inc.
11. Use long division to find the quotient and remainder when
x
4 + 5
x
2 – 3
x
+ 2 is divided by
x
– 2.
a.
x
3 2
x
2 9
x
15, R 32 b.
x
3 2
x
2 9
x
21, R 44 c.
x
3 2
x
2 9
x
21, R 44 d.
x
3 7
x
2 14
x
25, R 52 Copyright © 2009 Pearson Education, Inc.
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12. Use synthetic division to find the quotient and remainder when 3
x
3 – 6
x
2 + 4 is divided by
x
+ 3.
a. 3
x
2 15
x
b. 3
x
2 3
x
9, R 31 c. 3
x
15, R 49 d. 3
x
2 3
x
9, R 29 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 15
13. Use synthetic division to determine which number is a zero of
P
(
x
) =
x
3 –
x
2 – 22
x
+ 40.
a. 2 b. 8 c. 4 d. 5 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 16
14. Use synthetic division to find
P
( 5) for
P
(
x
) = 2
x
4 – 2
x
2 + 5
x
– 1. a. 1276 b. 1324 c. 174 d. 1326 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 17
15. Use synthetic division to find determine which number is a zero of
P
(
x
) =
x
3 – 6
x
2 + 3
x
+ 10.
a. 5 b. 1 c. 2 d. 10 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 18
16. Suppose that a polynomial function of 3 – 2
i
as zeros. Find one other zero. a. 2 b. 4 c. 3 + 2
i
d. 3 2
i
Copyright © 2009 Pearson Education, Inc.
Slide 4 - 19
17. Find a polynomial function of lowest degree with rational coefficients and 3 and 4
i
as some of its zeros.
a.
x
2 3
x
4
xi
12
i
b.
x
3 3
x
2 16
x
48 c.
x
3 3
x
2 16
x
48 d.
x
3 3
x
2 16
x
48 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 20
18. Use the rational zeros theorem to determine which number cannot be a zero of
P
(
x
) = 10
x
4 + 6
x
2 – 5
x
+ 2.
a. 1 5 b. 2 c. 5 d. 5 2 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 21
19. How many negative real zeros does Descartes’ rule of signs indicate
g
(
x
) =
x
5 + 4
x
4 – 2
x
3 + 3
x
2 – 6 has?
a. 1 b. 3 or 1 c. 5, 3 or 1 d. 2 or 0 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 22
20. Use the rational zeros theorem to determine which number cannot be a zero of
P
(
x
) = 4
x
4 + 3
x
2 +
x
– 3. a. 4 3 b. 3 4 c. 1 4 d. 3 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 23
21. Find the vertical asymptote for
f
(
x
) (
x
6 4) 2 a.
y
= 0 .
b.
x
= 4 c.
x
= 4 d.
x
3 8 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 24
a.
22. Which graph represents the polynomial function
f
(
x
)
x
2
x
3
x
3 4 .
b.
c.
Copyright © 2009 Pearson Education, Inc.
d.
Slide 4 - 25
c.
a.
23. Which graph represents the polynomial function
f
(
x
) (
x
6 2) 2 .
b.
d.
Slide 4 - 26
Copyright © 2009 Pearson Education, Inc.
24. Solve (
x
+ 4)(
x
– 2)(
x
– 6) ≤ 0.
a. b. c.
( , 4) (2,6) d. ( , 4] [2,6) Copyright © 2009 Pearson Education, Inc.
Slide 4 - 27
25. Solve 3
x
2 < 17
x
– 10.
a. , 2 3 b. 2 3 ,5 c.
d. 2 ,5 3 3 ,5 2 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 28
26. Solve
x
2
x
5 3.
a. 17 , 5 2 b. 17 2 c.
17 2 d. 17 2 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 29
27. Solve 3
x
2 >
x +
10.
a. b. 2, 5 3 5 3 c.
d. 3 5 , 5 3 , Copyright © 2009 Pearson Education, Inc.
Slide 4 - 30
28. Solve
x
1
x
5 6.
a. b. 5, 31 5 31 5 c.
d. 5, 31 5 31 , 5 Copyright © 2009 Pearson Education, Inc.
Slide 4 - 31
You should work all of the problems before checking your answers on the next slide.
Slide 4 - 32
Copyright © 2009 Pearson Education, Inc.
Answers: 1a 5a 9c 13d 17d 21b 25c Copyright © 2009 Pearson Education, Inc.
2c 6c 10a 14d 18c 22d 26a 3a 7b 11a 15c 19a 23b 27d 4b 8b 12a 16a 20a 24d 28b
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