Synthetic Division and the Remainder Theorem

One root of f(x) = x^3 - 4x^2 - 20x + 48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.

(x - 2)(x + 4)(x - 6)

Use synthetic division to solve mc003-1.jpg. What is the quotient?

2x^2 + 10x - 5

What dividend is represent by the synthetic division below? mc002-1.jpg

2x^3 + x

Use synthetic division to solve mc007-1.jpg. What is the quotient?

3x^3 + 2x + 5

One factor of f(x) = 4x^3 - 4x^2 - 16x + 16 is (x-2). What are all of the roots of the function. Use the Remainder Theorem.

x = -2, x = 1, or x = 2

One factor of f(x) = 5x^3 + 5x^2 - 170x + 280 is (x + 7). What are all of the roots of the function. Use the Remainder Theorem.

x = -7, x = 2, or x = 4

What remainder is represented by the synthetic division below? mc004-1.jpg

0

Use synthetic division to solve mc009-1.jpg. What is the quotient?

4x^2 - 27x + 167 - 996/x + 6

What divisor is represented by the synthetic division below? mc001-1.jpg

x + 5

If f(1) = 0, what are all the roots of the function f(x) = x^3 + 3x^2 - x - 3? Use the Remainder Theorem.

x = -3, x = -1, or x = 1