Polynomial And Rational Functions Test Bank Chapter 4

College Algebra, 5e (Young)

Chapter 4 Polynomial and Rational Functions

4.4 The Real Zeros of a Polynomial Function

1) For the polynomial f (x) = + 3 - 5x + 3, use synthetic division to find f (-3).

A) -18

B) -12

C) 18

D) 12

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply the remainder theorem to evaluate a polynomial function.

2) For the polynomial function f (x) = 5 +3x - 7, use synthetic division to find f (6).

A) 1091

B) 1104

C) 1182

D) 6

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply the remainder theorem to evaluate a polynomial function.

3) Determine whether the number 2 is a zero of f (x) = + 5- 22x + 16. If it is, find the other real zeros.

A) 2 is not a zero.

B) 2 is a zero and the others are 1 and -8.

C) 2 is a zero and the others are -1 and 8.

D) 2 is a zero and there are no other real zeros.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply the factor theorem.; Find the real zeros of a polynomial function.

4) Determine whether the number -7 is a zero of f (x) = + 3- 36x + 32. If it is, find the other real zeros.

A) -7 is not a zero.

B) -7 is a zero and the others are 3 and -36.

C) -7 is a zero and the other is 32.

D) -7 is a zero and there are no other real zeros.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply the factor theorem.; Factor a polynomial function. ; Find the real zeros of a polynomial function.

5) Determine whether -5 is a zero of the polynomial. If it is, then find the other real zeros.

P(x) = + 4 - 4x + 5

A) -5 is not a zero.

B) -5 is a zero and the other zeros are 4 and -4.

C) -5 is a zero and the other is 5.

D) -5 is a zero and there are no other real zeros.

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply the factor theorem.; Factor a polynomial function. ; Find the real zeros of a polynomial function.

6) Given that 4 is a zero of the polynomial P(x) = - 11 + 34x - 24, determine all other zeros.

A) -6 and 1

B) 6 and 1

C) -6 and -1

D) 6 and -1

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Factor a polynomial function. ; Find the real zeros of a polynomial function.

7) Use Descartes' rule of signs to determine the possible number of positive real zeros and negative real zeros. P(x) = 10 - 16 + 44x - 29.

A)

B)

C)

D)

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply Descartes' rule of signs to determine the possible combination of positive and negative real zeros.

8) Use Descartes' rule of signs to determine the possible number of positive real zeros and negative real zeros.

P(x) = 5 + 5 - 9x - 10

A)

B)

C)

D)

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply Descartes' rule of signs to determine the possible combination of positive and negative real zeros.

9) Use Descartes' rule of signs to determine the possible number of positive real zeros and negative real zeros.

P(x) = 6 + 3 + 5x - 5

A)

B)

C)

D)

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply Descartes' rule of signs to determine the possible combination of positive and negative real zeros.

10) Use Descartes' rule of signs to determine the possible number of positive real zeros, negative real zeros, and imaginary zeros.

P(x) = - 9 + 8x + 8

A)

B)

C)

D)

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply Descartes' rule of signs to determine the possible combination of positive and negative real zeros.

11) Use the rational zero theorem to list the possible rational zeros of the polynomial

A) {±1/3, ±1/11, ±1/7, ±1/33, ±1/77, ±1/21, ±1/231}

B) {±1, ±3, ±11, ±7}

C) {±1, ±3, ±11, ±7, ±33, ±77, ±21, ±231}

D) {±1/3, ±1/11, ±1/7}

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Use the rational zero (root) theorem to list possible rational zeros.

12) Use the rational zero theorem to list the possible rational zeros.

P(x) = 3 + 7 - 5x + 1

A) {±1, ±3}

B) {±1}

C) {±1, ±1/7}

D) {±1, ±1/3}

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Use the rational zero (root) theorem to list possible rational zeros.

13) Use the rational zero theorem to list the possible rational zeros.

P(x) = 11 - 8 + 2x - 77

A) {±1, ±1/11, ±7/11}

B) {±1, ±11, ±7, ±77}

C) {±1, ±11, ±7, ±77, ±1/11, ±7/11}

D) {±1, ±11, ±7}

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Use the rational zero (root) theorem to list possible rational zeros.

14) Given that -4 is a zero of the polynomial P(x) = + 7 + 14x + 8, determine all other zeros and write the polynomial in terms of a product of linear factors.

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Factor a polynomial function.

15) Use the rational zero theorem to list the possible rational zeros.

P(x) = + 4 + 8x + 143

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Use the rational zero (root) theorem to list possible rational zeros.

16) Use the intermediate value theorem to approximate the real zero in the indicated interval. Approximate to two decimal places if necessary.r

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Employ the intermediate value theorem to approximate a real zero.

17) Use the rational zero theorem to list the possible rational zeros.

P(x) = 4- 8 + 11x - 55

Diff: 2 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Use the rational zero (root) theorem to list possible rational zeros.

18) Use Descartes' rule of signs to determine the possible number of positive real zeros, negative real zeros, and imaginary zeros.

P(x) = - 3+ 3x + 6

Negative real 0s: 1

Imaginary 0s: 2 or 0

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply Descartes' rule of signs to determine the possible combination of positive and negative real zeros.

19) Use Descartes' rule of signs along with the rational root theorem to sketch a graph of the polynomial.

P(x) = - 3 - 4x + 12

Diff: 3 Var: 1

Chapter/Section: Ch 04, Sec 04

Learning Objective: Apply Descartes' rule of signs to determine the possible combination of positive and negative real zeros.

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