Solve 64+x^6

$$64+ { x }^{ 6 }$$

Factor

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

Solution Steps

Rewrite 64+x^{6} as \left(x^{2}\right)^{3}+4^{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). The following polynomials are not factored since they do not have any rational roots: x^{2}+4,x^{4}-4x^{2}+16.

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

Evaluate

$$x^{6}+64$$