x^4 - 16
This is the difference of two squares, which factors to
(x^2 + 4)(x^2 - 4)
You can't factor x^2 + 4 anymore, but x^2 - 4 is another difference of squares, which can be factored to (x + 2)(x - 2), the final answer is
(x^2 + 4)(x + 2)(x - 2)