There are several well-known criteria for a polynomial with integer coefficients to be irreducible over $\mathbb{Z}$, e.g., [Eisenstein's criterion][1]. I'm looking for the opposite: other than factorization, is there some sufficient condition to show that a given polynomial must be reducible? Ideally, I'd like some property that depends only on the coefficients appearing in the polynomial, like in Eisenstein's criterion. 


  [1]: https://en.wikipedia.org/wiki/Eisenstein%27s_criterion