Solve x^7-216x^4

$$x ^ { 7 } - 216 x ^ { 4 }$$

Factor

$$\left(x-6\right)\left(x^{2}+6x+36\right)x^{4}$$

Solution Steps

Factor out x^{4}.

$$x^{4}\left(x^{3}-216\right)$$

Consider x^{3}-216. Rewrite x^{3}-216 as x^{3}-6^{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).

$$\left(x-6\right)\left(x^{2}+6x+36\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+6x+36 is not factored since it does not have any rational roots.

$$x^{4}\left(x-6\right)\left(x^{2}+6x+36\right)$$

Evaluate

$$\left(x^{3}-216\right)x^{4}$$