Synthetic Division and the Remainder Theorem

Question 1

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

Revolt · Accepted Answer

x = –7, x = 2, or x = 4

Question 2

The volume of a rectangular prism is with height x + 2. Using synthetic division, what is the area of the base?

Revolt · Accepted Answer

2 x squared + 5 x minus 18

Question 3

Use synthetic division to solve . What is the quotient?

Revolt · Accepted Answer

4 x squared minus 27 x + 167 minus StartFraction 996 Over x + 6 EndFraction

Question 4

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

Revolt · Accepted Answer

f(–8) = 0

Question 5

What remainder is represented by the synthetic division below?

Revolt · Accepted Answer

0

Question 6

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

Revolt · Accepted Answer

A factor of f(x) is (x + 1).

Question 7

Use synthetic division to solve . What is the quotient?

Revolt · Accepted Answer

3 x cubed + 2 x + 5

Question 8

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

Revolt · Accepted Answer

(x – 2)(x + 4)(x – 6)

Question 9

Use synthetic division to solve . What is the quotient?

Revolt · Accepted Answer

2 x squared + 10 x minus 5

Question 10

What divisor is represented by the synthetic division below?

Revolt · Accepted Answer

x + 5

Synthetic Division and the Remainder Theorem Answers