Let f(x) and g(x) be two relatively prime polynomials having integer coefficients with g(0)≠0. The authors show that there is an N=N (f,g) such that if n>=N, then the non-reciprocal part of the polynomial f(x)x~n+g(x) is either irreducible or identically 1 or -1 with certain clear exceptions that arise from a theorem of Capelli. A version of this result is originally due to Andrzej Schinzel. The present paper gives a new approach that allows for an improved estimate on the value of N.
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