Solve 10x^4+10x=

$$10 x ^ { 4 } + 10 x =$$

Factor

$$10x\left(x+1\right)\left(x^{2}-x+1\right)$$

Solution Steps

Factor out 10.

$$10\left(x^{4}+x\right)$$

Consider x^{4}+x. Factor out x.

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

Consider x^{3}+1. Rewrite x^{3}+1 as x^{3}+1^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).

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

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

$$10x\left(x+1\right)\left(x^{2}-x+1\right)$$

Evaluate

$$10x\left(x^{3}+1\right)$$