H Alg II Mod 6 Quiz Polynomials Practice NAME _____________________
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Which of the following is a factor of ?
____ 2. Which of the following is NOT a factor of ?
____ 3. What is the remainder when is divided by ?
____ 4. For , . Which of the following must therefore be true?
A

is a factor of .

B

is a factor of .

C

is a factor of .

D

is a factor of .

____ 5. Divide:
____ 6. In the expression , when the first two terms are grouped, and the last two terms are grouped, what is the common binomial factor?
____ 7. What is the complete factorization of ?
A


C


B


D


____ 8. Factor .
____ 9. Divide.
____ 10. As a first step in factoring , substitute x for . What is the resulting trinomial expression?
Multiple Response
Identify one or more choices that best complete the statement or answer the question.
____ 1. Use the remainder theorem and the factor theorem to determine which of the following binomials are factors of .
Short Answer
1. Use the remainder theorem and the factor theorem to show that is a factor of . Then factor completely.
2. Divide.
3. Rewrite the expression as the sum of a polynomial and a rational expression whose numerator is a constant. Show your work. (Long Division)
4. Factor by grouping.
5. Divide.
Essay
1. Is a factor of ? How do you know?
Other
1. Use the remainder theorem and the factor theorem to determine whether the given binomial is a factor of the given polynomial.
H Alg II Mod 6 Quiz Polynomials Practice
Answer Section
MULTIPLE CHOICE
1. ANS: A PTS: 1 DIF: DOK 1 NAT: AAPR.B.2
2. ANS: B PTS: 1 DIF: DOK 2 NAT: AAPR.B.2
3. ANS: B PTS: 1 DIF: DOK 1 NAT: AAPR.B.2
4. ANS: D
The factor theorem says that for a polynomial and a number a, if and only if is a factor of . Since for this , must be a factor of .

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A

You cannot factor from the terms of .

B

You cannot factor from the terms of .

C

The factor theorem tells you that when , is a factor of .

D

That’s correct!

PTS: 1 DIF: DOK 1 NAT: AAPR.B.2 KEY: remainder theorem  factor theorem
5. ANS: B PTS: 1 DIF: DOK 1
OBJ: Using Synthetic Division to Divide by a Linear Binomial NAT: AAPR.D.6
LOC: MTH.C.10.05.08.03.03.003 TOP: Dividing Polynomials
6. ANS: C PTS: 1 DIF: DOK 1 NAT: ASSE.A.1b
KEY: complicated expressions
7. ANS: C PTS: 1 DIF: DOK 1 NAT: ASSE.A.2
8. ANS: D PTS: 1 DIF: DOK 2 OBJ: Factoring by Grouping
NAT: ASSE.A.2 LOC: MTH.C.10.05.08.03.04.011 TOP: Factoring Polynomials
9. ANS: B PTS: 1 DIF: DOK 1 NAT: AAPR.D.6
10. ANS: B PTS: 1 DIF: DOK 1 NAT: ASSE.A.1b
KEY: complicated expressions
MULTIPLE RESPONSE
1. ANS: A, D, F
The remainder theorem says that for a polynomial and a number a, the remainder on division of by is . The factor theorem states that if and only if is a factor of .
A:
B:
C:
D:
E:
F:

Feedback

Correct

That’s correct!

Incorrect

To see whether is a factor of , find and then use the remainder theorem and the factor theorem.

PTS: 2 DIF: DOK 1 NAT: AAPR.B.2 KEY: remainder theorem  factor theorem
SHORT ANSWER
1. ANS:
Use synthetic substitution to find :
The last number in the bottom row of the synthetic substitution array is . Since , is a factor of . The coefficients of the quotient when is divided by are the first three numbers in the bottom row of the synthetic substitution array. So, . Factoring the quadratic factor by inspection gives , the complete factorization of .
Rubric
1 point for showing is a factor of ;
1 point for finding as a factor;
1 point for finding as a factor
PTS: 3 DIF: DOK 2 NAT: AAPR.B.2
KEY: remainder theorem  factor theorem  synthetic substitution  factoring
2. ANS:
PTS: 1 DIF: DOK 1 NAT: AAPR.D.6
3. ANS:
Rubric
1 point for dividing correctly;
1 point for rewriting the expression in the correct form
PTS: 2 DIF: DOK 1 NAT: AAPR.D.6
KEY: rational expressions  dividing polynomials
4. ANS:
PTS: 1 DIF: DOK 1 NAT: ASSE.A.2
5. ANS:
PTS: 1 DIF: DOK 1 NAT: AAPR.D.6
LOC: NCTM.PSSM.00.MTH.912.ALG.2.c KEY: polynomial division
ESSAY
1. ANS:
If a polynomial simplifies to 0 when a is substituted for x, then is a factor of the polynomial.
is not a factor of .
PTS: 1 DIF: DOK 2 NAT: AAPR.B.2
OTHER
1. ANS:
a. No
b. Yes
c. Yes
d. No
e. Yes
PTS: 2 DIF: DOK 1 NAT: AAPR.B.2 KEY: remainder theorem  factor theorem
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