Solve 5x^5-625x^2

$$5 x ^ { 5 } - 625 x ^ { 2 }$$

Factor

$$5\left(x-5\right)x^{2}\left(x^{2}+5x+25\right)$$

Solution Steps

Factor out 5.

$$5\left(x^{5}-125x^{2}\right)$$

Consider x^{5}-125x^{2}. Factor out x^{2}.

$$x^{2}\left(x^{3}-125\right)$$

Consider x^{3}-125. Rewrite x^{3}-125 as x^{3}-5^{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).

$$\left(x-5\right)\left(x^{2}+5x+25\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+5x+25 is not factored since it does not have any rational roots.

$$5x^{2}\left(x-5\right)\left(x^{2}+5x+25\right)$$

Evaluate

$$5x^{2}\left(x^{3}-125\right)$$