Then non-reciprocal part of a polynomial \(f(x)\in{\mathbb Z}\) is defined as the polynomial \(f(x)\) removed of its reciprocal factors in \({\mathbb Z}[x]\) having a positive leading coefficient. A \(0,1\)-polynomial is a polynomial with each coefficient either \(0\) or \(1\).
The main result of the paper says if \(f(x)\) and \(g(x)\) are relatively prime \(0,1\)-polynomials with \(f(0)=g(0)=1\) and \(n>\deg g+2\max\{\deg f,\deg g\}\), then the non-reciprocal of \(f(x)x^n+g(x)\) is irreducible or identically \(1\). (For a related result consult [M. Filaseta, K. Ford and S. Konyagin, Ill. J. Math. 44, 633–643 (2000; Zbl 0966.11046)].)