Question 17314
You need to recognise this expression as the sum of two cubes.

{{{x^6 + 64 = (x^2)^3 + 4^3}}}

The sum of two cubes is factored as:

{{{A^3 + b^3 = (A + B)(A^2 - AB + B^2)}}}

{{{(x^2)^3 + 4^3 = (x^2 + 4)(x^4 - 4x^2 + 16)}}} Now factor the {{{(x^2 + 4)}}} as the sum of two squares.

{{{x^2 + 4 = (x + 2i)(x - 2i)}}}

Finally:

{{{x^6 + 64 = (x + 2i)(x - 2i)(x^4 - 4x^2 + 16)}}}