IMO 1976 LL USA40

Let g(x) be a fixed polynomial and define f(x) by f(x) =

IMO 1976 LL USA40

Origin: USA

Problem

Let g(x) be a fixed polynomial and define f(x) by f(x) = x2 + xg(x3). Show that f(x) is not divisible by x2 −x + 1.