Synthetic Division and the Remainder Theorem

Question 1

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

Revolt · Accepted Answer

f(–8) = 0

Question 2

What remainder is represented by the synthetic division below?

Revolt · Accepted Answer

0

Question 3

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 4

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 5

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

Question 6

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 7

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

Revolt · Accepted Answer

Answer image: https://media.edgenuity.com/evresources/3111-06-03/mc006-3.jpg

Question 8

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 9

Use synthetic division to solve . What is the quotient?

Revolt · Accepted Answer

2 x squared + 10 x minus 5

Question 10

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)

Synthetic Division and the Remainder Theorem Answers