Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible

Question

Let $A$ be a field and let $p(X)$ be a polynomial over $A$. Let $a\in A$.

Want to show:

$p(X)$ is irreducible if and only if $p(X+a)$ is irreducible.

I suspect that I should use the substitution principle somehow, but that's as far as I've come. Completely stumped.