Solve 2x^7+16x^4

$$2 x ^ { 7 } + 16 x ^ { 4 }$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(x^{7}+8x^{4}\right)$$

Consider x^{7}+8x^{4}. Factor out x^{4}.

$$x^{4}\left(x^{3}+8\right)$$

Consider x^{3}+8. Rewrite x^{3}+8 as x^{3}+2^{3}. The sum 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.

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

Evaluate

$$2\left(x^{3}+8\right)x^{4}$$