IMO 1993 - Shortlisted Problems Question 11

(IRE 1; IMO 1) Let $n\gt 1$ be an integer and let $f(x)=x^n+5x^{n-1}+3$. Prove that there do not exist polynomials $g(x),h(x)$, each having integer coefficients and degree at least one, such that $f(x)=g(x)h(x)$.