Solve 6x^5-48x^2

$$6 x ^ { 5 } - 48 x ^ { 2 }$$

Factor

$$6\left(x-2\right)x^{2}\left(x^{2}+2x+4\right)$$

Solution Steps

Factor out 6.

$$6\left(x^{5}-8x^{2}\right)$$

Consider x^{5}-8x^{2}. Factor out x^{2}.

$$x^{2}\left(x^{3}-8\right)$$

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.

$$6x^{2}\left(x-2\right)\left(x^{2}+2x+4\right)$$

Evaluate

$$6x^{2}\left(x^{3}-8\right)$$