In this article, we consider the polynomials of the form f(x) = a0+ a1x + a2X2+ ... + anxn∈ Z[x], where |a0| = |a1| + ... + |a0| and |ao| is a prime. We show that these polynomials have a cyclotomic factor whenever reducible. As a consequence, we give a simple procedure for checking the irreducibility of trinomials of this form and separability criterion for certain quadrinomials. © 2020 Societatea de Stiinte Matematice din Romania. All rights reserved.