AnswersAISD Algebra II B Credit Recovery 2026-2027Division of Polynomials

Synthetic Division and the Remainder Theorem Answers

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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
2
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Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?

A
x squared + x + 1 + StartFraction 2 Over x + 1 EndFraction
Option A
B
x squared minus x + 1
Option B
C
x squared + x + 1 + StartFraction 2 Over x minus 1 EndFraction
Option C
D
x cubed minus x squared + x minus 1
Option D
3

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)
4

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
5

What remainder is represented by the synthetic division below?

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

One root of is x = 2. What are all the roots of the function? Use the Remainder Theorem.

Question illustration
A
x = 2, x = 3, or x = 4
B
x = –2, x = –3, or x = –4
C
x = 1, x = 2, x = 3, or x = 13
D
x = –1, x = –2, x = –3, or x = –13
7

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
8

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
9

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
10

What divisor is represented by the synthetic division below?

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

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