An Irreducibility Lemma

We give a simple result (Lemma 2.5) which can be handy for proving certain polynomials are irreducible, or at least for putting constraints on the degrees of their possible factors. One can interpret our lemma as a generalization of the well-known Eisenstein Criterion. By way of illustration, we apply the lemma to prove the irreducibility of a certain family of hypergeometric polynomials.