Solve 5x^4-40x

$$5 x ^ { 4 } - 40 x$$

Factor

$$5x\left(x-2\right)\left(x^{2}+2x+4\right)$$

Solution Steps

Factor out 5.

$$5\left(x^{4}-8x\right)$$

Consider x^{4}-8x. Factor out x.

$$x\left(x^{3}-8\right)$$

Consider x^{3}-8. Rewrite x^{3}-8 as x^{3}-2^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).

$$\left(x-2\right)\left(x^{2}+2x+4\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+2x+4 is not factored since it does not have any rational roots.

$$5x\left(x-2\right)\left(x^{2}+2x+4\right)$$

Evaluate

$$5x\left(x^{3}-8\right)$$