This paper addresses a question recently posed by Hajir concerning the irreducibility of certain modifications F(x) of generalized Laguerre polynomials Ln(-n-1-r)(x) where r ≥ 0 is an integer. For a fixed r ≥ 0, we obtain lower bounds C(r) on n in terms of r such that F(x) is irreducible over the rationals for all n ≥ C(r). Furthermore, for r ≤ 3, it is shown that F(x) is either irreducible or is a product of a linear polynomial and a polynomial of degree n-1. The set of circumstances in which F(x) has a linear factor for r ≤ 3, is completely described. © 2020 World Scientific Publishing Company.