Irreducibility of Polynomials over Residue Class Ring

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Given some polynomial $P \in \mathbb{Z}/m\mathbb{Z}[T]$, is there an easy way to check if $P$ is irreducible? My understanding is that I cannot use Eisenstein's criterion because, in general, $\mathbb{Z}/m\mathbb{Z}$ is not a unique factorization domain.