Question

How do you factor `x^3 - x^2 -4x + 4`?

Answer 1

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

Explanation:

This factors by grouping:

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

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

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

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

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