AnswersAZ-Common Core Algebra II ADivision of Polynomials

Synthetic Division and the Remainder Theorem Answers

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1
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One factor of is (x + 7). What are all the roots of the function? Use the Remainder Theorem.

Question illustration
x
x = –4, x = –2, or x = 7
x
x = –7, x = 2, or x = 4
x
x = –7, x = 5, or x = 280
x
x = –280, x = –5, or x = 7
2
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The volume of a rectangular prism is with height x + 2. Using synthetic division, what is the area of the base?

Question illustration
A
2 x cubed + 13 x squared + 18 x
Option A
B
2 x cubed + 5 x squared minus 18 x
Option B
C
2 x squared + 13 x + 18
Option C
D
2 x squared + 5 x minus 18
Option D
3

Use synthetic division to solve . What is the quotient?

Question illustration
A
4 x squared minus 27 x + 167 minus StartFraction 996 Over x minus 6 EndFraction
Option A
B
4 x squared + 21 x + 131 + StartFraction 792 Over x + 6 EndFraction
Option B
C
4 x squared + 21 x + 131 + StartFraction 792 Over x minus 6 EndFraction
Option C
D
4 x squared minus 27 x + 167 minus StartFraction 996 Over x + 6 EndFraction
Option D
4

If (x + 8) is a factor of f(x), which of the following must be true?

A
Both x = –8 and x = 8 are roots of f(x).
B
Neither x = –8 nor x = 8 is a root of f(x).
C
f(–8) = 0
D
f(8) = 0
5

What remainder is represented by the synthetic division below?

Question illustration
A
–5
B
0
C
1
D
2
6

If –1 is a root of f(x), which of the following must be true?

A
A factor of f(x) is (x – 1).
B
A factor of f(x) is (x + 1).
C
Both (x – 1) and (x + 1) are factors of f(x).
D
Neither (x – 1) nor (x + 1) is a factor of f(x).
7

Use synthetic division to solve . What is the quotient?

Question illustration
A
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x + 2 EndFraction
Option A
B
3 x cubed + 2 x + 5
Option B
C
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x minus 2 EndFraction
Option C
D
3 x Superscript 4 Baseline + 2 x squared + 5 x
Option D
8

One root of is x = 6. What are all the factors of the function? Use the Remainder Theorem.

Question illustration
A
(x + 6)(x + 8)
B
(x – 6)(x – 8)
C
(x – 2)(x + 4)(x – 6)
D
(x + 2)(x – 4)(x + 6)
9

Use synthetic division to solve . What is the quotient?

Question illustration
A
2 x squared minus 2 x minus 29 + StartFraction 102 Over x + 3 EndFraction
Option A
B
2 x squared minus 2 x minus 29 + StartFraction 102 Over x minus 3 EndFraction
Option B
C
2 x cubed + 10 x squared minus 5 x
Option C
D
2 x squared + 10 x minus 5
Option D
10

What divisor is represented by the synthetic division below?

Question illustration
A
–5
B
5
C
x + 5
D
x – 5
11

The area of a rectangle is with length x + 3. Using synthetic division, what is the width of the rectangle?

Question illustration
A
5 x squared + 4 x minus 6
Option A
B
5 x squared + 34 x + 108 + StartFraction 306 Over x + 3 EndFraction
Option B
C
5 x cubed + 4 x squared minus 6 x
Option C
D
5 x squared + 34 x + 108 + StartFraction 306 Over x minus 3 EndFraction
Option D
12

The area of a rectangle is with length x + 3. Using synthetic division, what is the width of the rectangle?

Question illustration
A
5 x squared + 4 x minus 6
Option A
B
5 x squared + 34 x + 108 + StartFraction 306 Over x + 3 EndFraction
Option B
C
5 x cubed + 4 x squared minus 6 x
Option C
D
5 x squared + 34 x + 108 + StartFraction 306 Over x minus 3 EndFraction
Option D
13

Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

If f(1) = 0, what are all the roots of the function ? Use the Remainder Theorem.

Question illustration
A
x = –1, x = 1, or x = 3
B
x = –3, x = –1, or x = 1
C
x = –3 or x = 1
D
x = –1 or x = 3
15

What dividend is represented by the synthetic division below?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
16

Use synthetic division to solve . What is the quotient?

Question illustration
A
4 x squared minus 27 x + 167 minus StartFraction 996 Over x minus 6 EndFraction
Option A
B
4 x squared + 21 x + 131 + StartFraction 792 Over x + 6 EndFraction
Option B
C
4 x squared + 21 x + 131 + StartFraction 792 Over x minus 6 EndFraction
Option C
D
4 x squared minus 27 x + 167 minus StartFraction 996 Over x + 6 EndFraction
Option D
17

What dividend is represented by the synthetic division below?

Question illustration
A
Negative 10 x squared minus 5
Option A
B
2 x cubed + 10 x squared + x + 5
Option B
C
2 x squared + 1
Option C
D
2 x cubed + x
Option D
18

What divisor is represented by the synthetic division below?

Question illustration
A
–5
B
5
C
x + 5
D
x – 5
19

What remainder is represented by the synthetic division below?

Question illustration
A
–5
B
0
C
1
D
2
20

Use synthetic division to solve . What is the quotient?

Question illustration
A
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x + 2 EndFraction
Option A
B
3 x cubed + 2 x + 5
Option B
C
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x minus 2 EndFraction
Option C
D
3 x Superscript 4 Baseline + 2 x squared + 5 x
Option D

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