Synthetic Division and the Remainder Theorem

Question 1

Use synthetic division to solve . What is the quotient?

Revolt · Accepted Answer

3 x cubed + 2 x + 5

Question 2

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 3

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

Revolt · Accepted Answer

f(–8) = 0

Question 4

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 5

Use synthetic division to solve . What is the quotient?

Revolt · Accepted Answer

2 x squared + 10 x minus 5

Question 6

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

Revolt · Accepted Answer

x = –3, x = –1, or x = 1

Question 7

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

Revolt · Accepted Answer

x = –2, x = 1, or x = 2

Question 8

What remainder is represented by the synthetic division below?

Revolt · Accepted Answer

0

Question 9

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 10

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

Revolt · Accepted Answer

5 x squared + 4 x minus 6

Synthetic Division and the Remainder Theorem Answers