AnswersMathematics III ASynthetic Division and the Remainder Theorem

Synthetic Division and the Remainder Theorem Answers

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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
2
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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)
3

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
4

What remainder is represented by the synthetic division below?

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

One factor of is (x – 2). What are all the roots of the function? Use the Remainder Theorem.

Question illustration
A
x = 1, x = 2, or x = 4
B
x = –2, x = 1, or x = 2
C
x = 2, x = 4, or x = 16
D
x = –16, x = 2, or x = 16
6

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
7

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

Question illustration
A
x = –4, x = –2, or x = 7
B
x = –7, x = 2, or x = 4
C
x = –7, x = 5, or x = 280
D
x = –280, x = –5, or x = 7
8

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).
9

What divisor is represented by the synthetic division below?

Question illustration
A
–5
B
5
C
x + 5
D
x – 5
10

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

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