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

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

Factor

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

Solution Steps

Factor out x.

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

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

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

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

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

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

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