Solve x^4-64x

$$x ^ { 4 } - 64 x$$

Factor

$$x\left(x-4\right)\left(x^{2}+4x+16\right)$$

Solution Steps

Factor out x.

$$x\left(x^{3}-64\right)$$

Consider x^{3}-64. Rewrite x^{3}-64 as x^{3}-4^{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).

$$\left(x-4\right)\left(x^{2}+4x+16\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+4x+16 is not factored since it does not have any rational roots.

$$x\left(x-4\right)\left(x^{2}+4x+16\right)$$

Evaluate

$$x\left(x^{3}-64\right)$$