Getting an irreducible polynomial from co-prime polynomials

Question

Let $f$, $g$ both in $\Bbb{Z}[X]$ be 2 relatively prime polynomials with $\deg(f) > \deg(g)$. I need to show that for every sufficiently large prime $p$, the polynomial $pf+g$ is irreducible.
I tried divisibility criteria but even with simple cases, I didn't succeed, so I think it must be something else.