Perron's irreducibility criterion

Perron's irreducibility criterion is a sufficient condition for a polynomial to be irreducible in ${\displaystyle \mathbb {Z} [x]}$—that is, for it to be unfactorable into the product of lower-degree polynomials with integer coefficients.

This criterion is applicable only to monic polynomials. However, unlike other commonly used criteria, Perron's criterion does not require any knowledge of prime decomposition of the polynomial's coefficients.