Solve x^4-x^3-x+x^2

$$x ^ { 4 } - x ^ { 3 } - x + x ^ { 2 }$$

Factor

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

Solution Steps

Factor out x.

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

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

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

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

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

Rewrite the complete factored expression. Polynomial x^{2}+1 is not factored since it does not have any rational roots.

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

Evaluate

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