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

Sep 25, 2016

${x}^{3} - {x}^{2} - 4 x + 4 = \left(x - 2\right) \left(x + 2\right) \left(x - 1\right)$

#### Explanation:

This factors by grouping:

${x}^{3} - {x}^{2} - 4 x + 4 = \left({x}^{3} - {x}^{2}\right) - \left(4 x - 4\right)$

$\textcolor{w h i t e}{{x}^{3} - {x}^{2} - 4 x + 4} = {x}^{2} \left(x - 1\right) - 4 \left(x - 1\right)$

$\textcolor{w h i t e}{{x}^{3} - {x}^{2} - 4 x + 4} = \left({x}^{2} - 4\right) \left(x - 1\right)$

$\textcolor{w h i t e}{{x}^{3} - {x}^{2} - 4 x + 4} = \left({x}^{2} - {2}^{2}\right) \left(x - 1\right)$

$\textcolor{w h i t e}{{x}^{3} - {x}^{2} - 4 x + 4} = \left(x - 2\right) \left(x + 2\right) \left(x - 1\right)$