Hi, this was a problem on an exam, and I wasn't sure how to do it.

The problem is as follows:

Let $\displaystyle f(y)=y^p-x \in Z_p(x)[y]$, where $\displaystyle p$ is prime. Show that $\displaystyle f(y)$ is irreducible in $\displaystyle Z_p(x)$.

I'm lost on this one. I feel like I should assume that it's reducible, which implies that $\displaystyle f(y)$ can be factored into irreducibles of lesser degree, but somehow there aren't any products of irreducibles that give us $\displaystyle f(y)$. Unfortunately, I don't know how to show the "somehow" part

Hope someone can help! Thanks!