Question

Factor the polynomial F(x) =x^3-x^2-4x+4 completely.

Part 1: Find and list all the possible roots of F(x).

Part 2: Use the remainder Theorem to determine which of the roots from Part I are roots of F(x).

Part 3:Factor the polynomial F(x)=x^3-x^2-4x+4 completely show your work.

Part 4:check your answer from Part 3 by multiplying the factors. Show your work

Answer 1

Explanation:

PART 1:

Possible roots by noticing the coefficient of first term:

x = 1, -1

PART 2:

1 | 1 -1 -4 4

1 0 -4

1 0 -4 0

The remainder is zero, hence one factor is (x-1)

PART 3:

`x^3-x^2-4x+4=(x^2-4)(x-1)\\\\x^3-x^2-4x+4=(x+2)(x-2)(x-1)`

PART 4:

`f(x)=(x+2)(x-2)(x-1)\\\\=(x^2-4)(x-1)\\\\=x^3-4x-x^2+4\\\\=x^3-x^2-4x+4`