  In this article, we consider the polynomials of the form
$f(x)=a_0+a_1x+a_2x^2+\cdots+a_nx^n\in \mathbb{Z}[x],$ where
$|a_0|=|a_1|+\dots+|a_n|$ and $|a_0|$ 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.
