Solve x^3-x^2-x+1

$$x ^ { 3 } - x ^ { 2 } - x + 1$$

Factor

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

Solution Steps

Do the grouping x^{3}-x^{2}-x+1=\left(x^{3}-x^{2}\right)+\left(-x+1\right), and factor out x^{2} in the first and -1 in the second group.

$$x^{2}\left(x-1\right)-\left(x-1\right)$$

Factor out common term x-1 by using distributive property.

$$\left(x-1\right)\left(x^{2}-1\right)$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

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

Evaluate

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