# How do you factor g(x)=x^3-x^2-x+1?

Mar 16, 2018

color(green)(g(x) = (x + 1) * (x- 1)^2

#### Explanation:

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

$g \left(x\right) = {x}^{2} \left(x - 1\right) - 1 \left(x - 1\right)$ Taking common ${x}^{2}$ out.

$\implies \left({x}^{2} - 1\right) \cdot \left(x - 1\right)$ Separating common terms.

As per identity, $\left(x + 1\right) \cdot \left(x - 1\right) = {x}^{2} - 1$

Hence $g \left(x\right) \implies \left(x + 1\right) \left(x - 1\right) \left(x - 1\right)$

color(green)(g(x) = (x + 1) * (x- 1)^2