How to prove the modular reduction of the coefficients of a polynomials in $\mathbb{Z}$ being irreducible implies irreducibility in $\mathbb{Q}[x]$

Question

I would like a hint on how to start this problem:

If $\sigma _m $ takes polynomials in $\mathbb{Z}$ and maps them to $\mathbb{Z}_m$ I want to show that if $\sigma _m (f(x))$ and $f(x)$ have the same degree and $\sigma _m (f(x))$ does not factor in $\mathbb{Z}_m[x]$ then $f(x)$ is irreducible in $\mathbb{Q}[x]$.

I have already shown that $\sigma _m$ is a ring homomorphism.