Solve f(x)=-x^3+x^2+x-1

$$f ( x ) = - x ^ { 3 } + x ^ { 2 } + x - 1$$

Factor

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

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.

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

Evaluate

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