Let F-q be a finite field of odd order q and m, n be positive integers. In this paper, the irreducible factorization of X-2m P-n - 1 over Fq is given in a very explicit form, where p is an odd prime divisor of q-1. It is shown that all the irreducible factors of (XPn)-P-2m - 1 over F-q are either binomials or trinomials. (C) 2013 Elsevier Inc. All rights reserved.