We investigate when mulitplication by a polynomialf(X) defines a surjective endomorphism on the inverse polynomials moduleM[X-1]. WhenMis artinian or even a module which has a secondary represention, this is equivalent toM=c(f)M, wherec(f), the content off, is the ideal generated by the coefficients inf. A criterion for the surjectivity of the endomorphism on End(L,M) induced by anendomorhismfon a finite free mduleLis also given.