Prove or disprove: $x^{p}+a$ is irreducible where $a\in \mathbb{Z}_{p}$.
This is what I've done so far:
By Fermat's Little Theorem, since $a^{p-1}\equiv 1$ (mod $p$) or $a^{p}\equiv a$ (mod $p$), then $x^{p}+a^{p}$ (mod $p$). Should I use Eisenstein's criterion on this polynomial? Any hints? I feel like this polynomial is reducible.