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