Chapter6 Test

Multiple Choice

*Identify the choice that best completes the statement or answers the question.*

____ 1. Determine which binomial is a factor of .

a. / x + 5 / b. / x + 20 / c. / x – 24 / d. / x – 5____ 2. Find the zeros of . Then graph the equation.

a. / –4, –2, 4/ c. / –4, –2

b. / 0, –4, –2

/ d. / 0, 4, 2

Short Answer

3. Classify –3x5 + 4x3 + x2 + 9 by degree and by number of terms.

4. Classify –9x4 + 7x3 – 6x2 by degree and by number of terms.

5. Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.

6. Write the expression (x + 5)(x + 2) as a polynomial in standard form.

7. Write 2x3 + 14x2 + 20x in factored form.

8. Write a polynomial function in standard form with zeros at 5, –4, and –3.

9. Find the zeros of and state the multiplicity.

10. Divide by x + 2.

11. Divide by x – 2.

**Divide using synthetic division.**

12.

13.

**Factor the expression.**

14.

15.

16. Solve . Find all complex roots.

17. Solve . Find all complex roots.

18. Solve .

19. Find the zeros of . Then graph the equation.

**Use Pascal’s Triangle to expand the binomial.**

20.

21.

22.

23. A polynomial equation with rational coefficients has the roots . Find two additional roots.

24. A polynomial equation with rational coefficients has the roots . Find two additional roots.

Chapter6 Test

Answer Section

MULTIPLE CHOICE

1. ANS: D PTS: 1 DIF: L2 REF: 6-3 Dividing Polynomials

OBJ: 6-3.1 Using Long Division STA: CA A2 3.0 TOP: 6-3 Example 2

KEY: division of polynomials | factoring a polynomial | polynomial

2. ANS: B PTS: 1 DIF: L2 REF: 6-2 Polynomials and Linear Factors

OBJ: 6-2.2 Factors and Zeros of a Polynomial Function STA: CA A2 10.0

TOP: 6-2 Example 4

KEY: Zero Product Property | polynomial function | zeros of a polynomial function | graphing

SHORT ANSWER

3. ANS:

quintic polynomial of 4 terms

PTS: 1 DIF: L2 REF: 6-1 Polynomial Functions

OBJ: 6-1.1 Exploring Polynomial Functions STA: CA A2 3.0

TOP: 6-1 Example 1 KEY: degree of a polynomial | polynomial

4. ANS:

quartic trinomial

PTS: 1 DIF: L2 REF: 6-1 Polynomial Functions

OBJ: 6-1.1 Exploring Polynomial Functions STA: CA A2 3.0

TOP: 6-1 Example 1 KEY: degree of a polynomial | polynomial

5. ANS:

20x5 – 8x4; quintic binomial

PTS: 1 DIF: L3 REF: 6-1 Polynomial Functions

OBJ: 6-1.1 Exploring Polynomial Functions STA: CA A2 3.0

TOP: 6-1 Example 1

KEY: degree of a polynomial | polynomial | standard form of a polynomial

6. ANS:

x2 + 7x + 10

PTS: 1 DIF: L2 REF: 6-2 Polynomials and Linear Factors

OBJ: 6-2.1 The Factored Form of a Polynomial STA: CA A2 10.0

TOP: 6-2 Example 1 KEY: polynomial | standard form of a polynomial

7. ANS:

2x(x + 2)(x + 5)

PTS: 1 DIF: L2 REF: 6-2 Polynomials and Linear Factors

OBJ: 6-2.1 The Factored Form of a Polynomial STA: CA A2 10.0

TOP: 6-2 Example 2 KEY: factoring a polynomial | polynomial

8. ANS:

PTS: 1 DIF: L2 REF: 6-2 Polynomials and Linear Factors

OBJ: 6-2.2 Factors and Zeros of a Polynomial Function STA: CA A2 10.0

TOP: 6-2 Example 5

KEY: polynomial function | standard form of a polynomial | zeros of a polynomial function

9. ANS:

–2, multiplicity 6; –3, multiplicity 4

PTS: 1 DIF: L2 REF: 6-2 Polynomials and Linear Factors

OBJ: 6-2.2 Factors and Zeros of a Polynomial Function STA: CA A2 10.0

TOP: 6-2 Example 6

KEY: polynomial function | zeros of a polynomial function | multiplicity | multiple zero

10. ANS:

, R 23

PTS: 1 DIF: L2 REF: 6-3 Dividing Polynomials

OBJ: 6-3.1 Using Long Division STA: CA A2 3.0 TOP: 6-3 Example 1

KEY: polynomial | division of polynomials

11. ANS:

, R 10

PTS: 1 DIF: L2 REF: 6-3 Dividing Polynomials

OBJ: 6-3.1 Using Long Division STA: CA A2 3.0 TOP: 6-3 Example 1

KEY: polynomial | division of polynomials

12. ANS:

PTS: 1 DIF: L3 REF: 6-3 Dividing Polynomials

OBJ: 6-3.2 Using Synthetic Division STA: CA A2 3.0 TOP: 6-3 Example 3

KEY: division of polynomials | polynomial | synthetic division

13. ANS:

PTS: 1 DIF: L3 REF: 6-3 Dividing Polynomials

OBJ: 6-3.2 Using Synthetic Division STA: CA A2 3.0 TOP: 6-3 Example 3

KEY: division of polynomials | polynomial | synthetic division

14. ANS:

PTS: 1 DIF: L2 REF: 6-4 Solving Polynomial Equations

OBJ: 6-4.2 Solving Equations by Factoring STA: CA A2 4.0

TOP: 6-4 Example 3 KEY: polynomial | factoring a polynomial

15. ANS:

PTS: 1 DIF: L2 REF: 6-4 Solving Polynomial Equations

OBJ: 6-4.2 Solving Equations by Factoring STA: CA A2 4.0

TOP: 6-4 Example 3 KEY: factoring a polynomial | polynomial

16. ANS:

,

PTS: 1 DIF: L2 REF: 6-4 Solving Polynomial Equations

OBJ: 6-4.2 Solving Equations by Factoring STA: CA A2 4.0

TOP: 6-4 Example 4 KEY: factoring a polynomial | polynomial function

17. ANS:

,

PTS: 1 DIF: L2 REF: 6-4 Solving Polynomial Equations

OBJ: 6-4.2 Solving Equations by Factoring STA: CA A2 4.0

TOP: 6-4 Example 4 KEY: factoring a polynomial | polynomial function

18. ANS:

2, –2, 6, –6

PTS: 1 DIF: L2 REF: 6-4 Solving Polynomial Equations

OBJ: 6-4.2 Solving Equations by Factoring STA: CA A2 4.0

TOP: 6-4 Example 6 KEY: factoring a polynomial | polynomial

19. ANS:

0, 5, 2

PTS: 1 DIF: L2 REF: 6-2 Polynomials and Linear Factors

OBJ: 6-2.2 Factors and Zeros of a Polynomial Function STA: CA A2 10.0

TOP: 6-2 Example 4

KEY: Zero Product Property | polynomial function | zeros of a polynomial function | graphing

20. ANS:

PTS: 1 DIF: L2 REF: 6-8 The Binomial Theorem

OBJ: 6-8.1 Binomial Expansion and Pascal's Triangle STA: CA A2 20.0

TOP: 6-8 Example 2 KEY: Pascal's Triangle | binomial expansion

21. ANS:

PTS: 1 DIF: L2 REF: 6-8 The Binomial Theorem

OBJ: 6-8.1 Binomial Expansion and Pascal's Triangle STA: CA A2 20.0

TOP: 6-8 Example 1 KEY: Pascal's Triangle | binomial expansion

22. ANS:

PTS: 1 DIF: L2 REF: 6-8 The Binomial Theorem

OBJ: 6-8.1 Binomial Expansion and Pascal's Triangle STA: CA A2 20.0

TOP: 6-8 Example 1 KEY: Pascal's Triangle | binomial expansion

23. ANS:

PTS: 1 DIF: L2 REF: 6-5 Theorems About Roots of Polynomial Equations

OBJ: 6-5.2 Irrational Root Theorem and Imaginary Root Theorem

STA: CA A2 5.0 | CA A2 6.0 | CA A2 8.0 TOP: 6-5 Example 3

KEY: polynomial function | solving equations | Irrational Root Theorem | conjugates

24. ANS:

PTS: 1 DIF: L2 REF: 6-5 Theorems About Roots of Polynomial Equations

OBJ: 6-5.2 Irrational Root Theorem and Imaginary Root Theorem

STA: CA A2 5.0 | CA A2 6.0 | CA A2 8.0 TOP: 6-5 Example 3

KEY: polynomial function | solving equations | Irrational Root Theorem | conjugates