H alg II mod 6 Quiz Polynomials Practice name multiple Choice



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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 ?

A



B



C



D

x +2

____ 2. Which of the following is NOT a factor of ?



A



C



B



D



____ 3. What is the remainder when is divided by ?



A



C



B



D

25

____ 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:



A



C



B



D


____ 6. In the expression , when the first two terms are grouped, and the last two terms are grouped, what is the common binomial factor?



A



C



B



D



____ 7. What is the complete factorization of ?



A



C



B



D


____ 8. Factor .



A



C

()

B

()

D


____ 9. Divide.





A



C



B



D


____ 10. As a first step in factoring , substitute x for . What is the resulting trinomial expression?



A



C



B



D





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 .


A



B



C



D



E



F




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.


a.

;

Yes

No

b.

;

Yes

No





































H Alg II Mod 6 Quiz Polynomials Practice

Answer Section
MULTIPLE CHOICE
1. ANS: A PTS: 1 DIF: DOK 1 NAT: A-APR.B.2
2. ANS: B PTS: 1 DIF: DOK 2 NAT: A-APR.B.2
3. ANS: B PTS: 1 DIF: DOK 1 NAT: A-APR.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 .







Feedback__A'>Feedback

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: A-APR.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: A-APR.D.6

LOC: MTH.C.10.05.08.03.03.003 TOP: Dividing Polynomials
6. ANS: C PTS: 1 DIF: DOK 1 NAT: A-SSE.A.1b

KEY: complicated expressions


7. ANS: C PTS: 1 DIF: DOK 1 NAT: A-SSE.A.2
8. ANS: D PTS: 1 DIF: DOK 2 OBJ: Factoring by Grouping

NAT: A-SSE.A.2 LOC: MTH.C.10.05.08.03.04.011 TOP: Factoring Polynomials


9. ANS: B PTS: 1 DIF: DOK 1 NAT: A-APR.D.6
10. ANS: B PTS: 1 DIF: DOK 1 NAT: A-SSE.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: A-APR.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: A-APR.B.2

KEY: remainder theorem | factor theorem | synthetic substitution | factoring


2. ANS:

PTS: 1 DIF: DOK 1 NAT: A-APR.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: A-APR.D.6

KEY: rational expressions | dividing polynomials
4. ANS:

PTS: 1 DIF: DOK 1 NAT: A-SSE.A.2


5. ANS:

PTS: 1 DIF: DOK 1 NAT: A-APR.D.6

LOC: NCTM.PSSM.00.MTH.9-12.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: A-APR.B.2
OTHER
1. ANS:

a. No


b. Yes

c. Yes


d. No

e. Yes


PTS: 2 DIF: DOK 1 NAT: A-APR.B.2 KEY: remainder theorem | factor theorem

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