I know that Eisenstein criterion is sufficient condition to determine whether a polynomial is irreducible in $\mathbb Q$.
But I do not know if the same approach can be applied to a body such $\mathbb{Z}_{p}$.
For example the polynomial:
$x^5+2x^4+2x^3+2x^2+2x+2 \in \mathbb{Z}_{3}[x]$
with $p = 2$
Eisenstein criterion would say that it is irreducible.