Chapter6 Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Classify –3x5 + 4x3 + x2 + 9 by degree and by number of terms.
a. quadratic binomial
c. quintic polynomial of 4 terms
b. quartic polynomial of 4 terms
d. cubic binomial
____
2. Write the expression (x + 5)(x + 2) as a polynomial in standard form.
a. x2 + 3x + 10
c. x2 + 7x + 10
b. x2 – 3x + 7
d. x2 + 3x – 3
____
3. Write 2x3 + 14x2 + 20x in factored form.
a. 2x(x + 5)(x + 2)
b. 2x(x + 5)(x – 2)
c. 5x(x + 2)(x + 2)
d. 2x(x + 2)(x + 5)
____
4. Write a polynomial function in standard form with zeros at 5, –4, and –3.
a.
c.
b.
d.
____
5. Find the zeros of
a. –2, multiplicity 6; 4, multiplicity –3
b. –2, multiplicity 6; –3, multiplicity 4
c. 6, multiplicity –2; –3, multiplicity 4
d. 6, multiplicity –2; 4, multiplicity –3
____
6. Divide
a.
b.
and state the multiplicity.
by x + 2.
, R –29
c.
d.
, R 23
Divide using synthetic division.
____
7.
a.
b.
c.
d.
Factor the expression.
____
____
8.
a.
b.
c.
d.
a.
b.
c.
d.
9.
____ 10. Solve
a. no solution
. Find all complex roots.
c.
5 5
 ,
3 3
b.
d.
5
 ,
3
____ 11. Solve
a. 2, –2, 6, –6
b. no solution
5
,
3
.
c. 2, –2
d. 2, –6
____ 12. Find the zeros of
a. 5, 2, –5
. Then graph the equation.
c. 5, 2
y
–6
–4
y
6
6
4
4
2
2
–2
2
4
6
–6
x
–4
–2
–2
–2
–4
–4
–6
–6
y
a.
b.
c.
d.
____ 14.
a.
b.
6
x
–4
2
4
6
x
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
Use Pascal’s Triangle to expand the binomial.
____ 13.
4
d. 0, –5, –2
b. 0, 5, 2
–6
2
c.
d.
____ 15.
a.
b.
c.
d.
____ 16. Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.
a. 2x + 9x4; quintic binomial
c. 2x5 – 8x4; quintic trinomial
5
4
b. 20x – 8x ; quintic binomial
d. 20x5 – 10x4; quartic binomial
____ 17. Determine which binomial is a factor of
a. x + 5
b. x + 20
.
c. x – 24
d. x – 5
____ 18. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
. Do not find the actual roots.
a. –4, –2, –1, 1, 2, 4
c. 1, 2, 4
b. no roots
d. –4, –1, 1, 4
____ 19. Find the rational roots of
a. 2, 6
b. –6, –2
.
c. –2, 6
d. –6, 2
Find the roots of the polynomial equation.
____ 20.
a. –3 ± 5i, –4
b. 3 ± 5i, –4
c. –3 ± i, 4
d. 3 ± i, 4
a.
c.
b.
d.
a.
b.
c.
d.
____ 21.
____ 22.
____ 23. A polynomial equation with rational coefficients has the roots
a.
c.
b.
d.
. Find two additional roots.
____ 24. For the equation
, find the number of complex roots and the possible number of real
roots.
a. 4 complex roots; 0, 2 or 4 real roots
b. 4 complex roots; 1 or 3 real roots
c. 3 complex roots; 1 or 3 real roots
d. 3 complex roots; 0, 2 or 4 real roots
For the equation, find the number of complex roots, the possible number of real roots, and the possible
rational roots.
____ 25.
a. 7 complex roots; 1, 3, 5, or 7 real roots; possible rational roots: ±1, ±5
b. 7 complex roots; 2, 4, or 6 real roots; possible rational roots: ±1, ±5
c.
5 complex roots; 1, 3, or 5 real roots; possible rational roots:
, ±1, ±5
d. 5 complex roots; 1, 3, or 5 real roots; possible rational roots: ±1, ±5
____ 26.
a.
b.
c.
d.
6 complex roots; 2, 4, or 6 real roots; possible rational roots:
6 complex roots; 2, 4, or 6 real roots; possible rational roots:
6 complex roots; 0, 2, 4, or 6 real roots; possible rational roots:
6 complex roots; 0, 2, 4, or 6 real roots; possible rational roots:
____ 27. Find all zeros of
a.
b.
____ 28. Use the Binomial Theorem to expand
a.
b.
c.
d.
.
c.
d.
.
Chapter6 Test
Answer Section
MULTIPLE CHOICE
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12. ANS:
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13. ANS:
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14. ANS:
OBJ:
C
PTS: 1
DIF: L2
REF: 6-1 Polynomial Functions
6-1.1 Exploring Polynomial Functions
STA: CA A2 3.0
6-1 Example 1
KEY: degree of a polynomial | polynomial
C
PTS: 1
DIF: L2
REF: 6-2 Polynomials and Linear Factors
6-2.1 The Factored Form of a Polynomial
STA: CA A2 10.0
6-2 Example 1
KEY: polynomial | standard form of a polynomial
D
PTS: 1
DIF: L2
REF: 6-2 Polynomials and Linear Factors
6-2.1 The Factored Form of a Polynomial
STA: CA A2 10.0
6-2 Example 2
KEY: factoring a polynomial | polynomial
D
PTS: 1
DIF: L2
REF: 6-2 Polynomials and Linear Factors
6-2.2 Factors and Zeros of a Polynomial Function
STA: CA A2 10.0
6-2 Example 5
polynomial function | standard form of a polynomial | zeros of a polynomial function
B
PTS: 1
DIF: L2
REF: 6-2 Polynomials and Linear Factors
6-2.2 Factors and Zeros of a Polynomial Function
STA: CA A2 10.0
6-2 Example 6
polynomial function | zeros of a polynomial function | multiplicity | multiple zero
D
PTS: 1
DIF: L2
REF: 6-3 Dividing Polynomials
6-3.1 Using Long Division
STA: CA A2 3.0
TOP: 6-3 Example 1
polynomial | division of polynomials
A
PTS: 1
DIF: L3
REF: 6-3 Dividing Polynomials
6-3.2 Using Synthetic Division
STA: CA A2 3.0
TOP: 6-3 Example 3
division of polynomials | polynomial | synthetic division
B
PTS: 1
DIF: L2
REF: 6-4 Solving Polynomial Equations
6-4.2 Solving Equations by Factoring
STA: CA A2 4.0
6-4 Example 3
KEY: polynomial | factoring a polynomial
B
PTS: 1
DIF: L2
REF: 6-4 Solving Polynomial Equations
6-4.2 Solving Equations by Factoring
STA: CA A2 4.0
6-4 Example 3
KEY: factoring a polynomial | polynomial
B
PTS: 1
DIF: L2
REF: 6-4 Solving Polynomial Equations
6-4.2 Solving Equations by Factoring
STA: CA A2 4.0
6-4 Example 4
KEY: factoring a polynomial | polynomial function
A
PTS: 1
DIF: L2
REF: 6-4 Solving Polynomial Equations
6-4.2 Solving Equations by Factoring
STA: CA A2 4.0
6-4 Example 6
KEY: factoring a polynomial | polynomial
B
PTS: 1
DIF: L2
REF: 6-2 Polynomials and Linear Factors
6-2.2 Factors and Zeros of a Polynomial Function
STA: CA A2 10.0
6-2 Example 4
Zero Product Property | polynomial function | zeros of a polynomial function | graphing
C
PTS: 1
DIF: L2
REF: 6-8 The Binomial Theorem
6-8.1 Binomial Expansion and Pascal's Triangle
STA: CA A2 20.0
6-8 Example 2
KEY: Pascal's Triangle | binomial expansion
D
PTS: 1
DIF: L2
REF: 6-8 The Binomial Theorem
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
15. ANS: A
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
16. ANS: B
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
17. 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
18. ANS: A
PTS: 1
DIF: L2
REF: 6-5 Theorems About Roots of Polynomial Equations
OBJ: 6-5.1 The Rational Root Theorem
STA: CA A2 5.0 | CA A2 6.0 | CA A2 8.0
TOP: 6-5 Example 1
KEY: polynomial function | root of a function | solving equations | Rational Root Theorem
19. ANS: B
PTS: 1
DIF: L2
REF: 6-5 Theorems About Roots of Polynomial Equations
OBJ: 6-5.1 The Rational Root Theorem
STA: CA A2 5.0 | CA A2 6.0 | CA A2 8.0
TOP: 6-5 Example 1
KEY: polynomial function | Rational Root Theorem | root of a function | solving equations
20. ANS: B
PTS: 1
DIF: L2
REF: 6-5 Theorems About Roots of Polynomial Equations
OBJ: 6-5.1 The Rational Root Theorem
STA: CA A2 5.0 | CA A2 6.0 | CA A2 8.0
TOP: 6-5 Example 2
KEY: polynomial function | Rational Root Theorem | solving equations | root of a function
21. ANS: A
PTS: 1
DIF: L2
REF: 6-5 Theorems About Roots of Polynomial Equations
OBJ: 6-5.1 The Rational Root Theorem
STA: CA A2 5.0 | CA A2 6.0 | CA A2 8.0
TOP: 6-5 Example 2
KEY: polynomial function | Rational Root Theorem | root of a function
22. ANS: D
PTS: 1
DIF: L2
REF: 6-5 Theorems About Roots of Polynomial Equations
OBJ: 6-5.1 The Rational Root Theorem
STA: CA A2 5.0 | CA A2 6.0 | CA A2 8.0
TOP: 6-5 Example 2
KEY: polynomial function | Rational Root Theorem | solving equations | root of a function
23. ANS: C
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: A
PTS: 1
DIF: L2
REF: 6-6 The Fundamental Theorem of Algebra
OBJ: 6-6.1 The Fundamental Theorem of Algebra TOP:
6-6 Example 1
KEY: Fundamental Theorem of Algebra | Imaginary Root Theorem | Rational Root Theorem | root of a
function | polynomial function
25. ANS: A
PTS: 1
DIF: L2
REF: 6-6 The Fundamental Theorem of Algebra
OBJ: 6-6.1 The Fundamental Theorem of Algebra TOP:
6-6 Example 1
KEY: Fundamental Theorem of Algebra | Imaginary Root Theorem | Rational Root Theorem | root of a
function | polynomial function
26. ANS: D
PTS: 1
DIF: L3
REF: 6-6 The Fundamental Theorem of Algebra
OBJ: 6-6.1 The Fundamental Theorem of Algebra TOP:
6-6 Example 1
KEY: Fundamental Theorem of Algebra | Imaginary Root Theorem | Rational Root Theorem | root of a
function | polynomial function
27. ANS: B
PTS: 1
DIF: L2
REF: 6-6 The Fundamental Theorem of Algebra
OBJ: 6-6.1 The Fundamental Theorem of Algebra TOP:
6-6 Example 2
KEY: Fundamental Theorem of Algebra | Rational Root Theorem | polynomial function | root of a function |
zeros of a polynomial function
28. ANS: D
PTS: 1
DIF: L2
REF: 6-8 The Binomial Theorem
OBJ: 6-8.2 The Binomial Theorem
STA: CA A2 20.0 TOP: 6-8 Example 3
KEY: Pascal's Triangle | binomial expansion