How do I go about factoring $x^n-4n-4$?

Question

How do I factor $$x^n-4n-4$$ (please provide steps)

I have a test in a few hours and would just like to understand this asap.

Thank you.

Answer 1

To factor

$$x^n-4(n+1)$$

find the $n$ $n$-th roots of $4(n+1)$, call them $w_0,w_1,\cdots,w_{n-1}$, then

$$x^n-4(n+1)=(x-w_0)(x-w_1)\cdots(x-w_{n-1})$$

You know that

$$ w_0=\sqrt[n]{4(n+1)}e^{2\pi i/n} $$

etc.