Factoring a complex polynomial

Question

Factorize the polynomial :

$$ p(x) = x^{5} - x^{4}+ 4x - 4 $$

In real factors in the lowest degree possible.

So in previous questions I have been given at least one rot so that I can factorize it with polynomial division. But how do I do now?

Answer 1

$$x^5-x^4+4x-4=x^4(x-1)+4(x-1)=(x-1)(x^4+4)$$

Again, $$x^4+4=(x^2)^2+2^2=(x^2+2)^2-2\cdot x^2\cdot 2=(x^2+2)^2-(2x)^2$$