SCHWEITZER 1998 Problem 2

For any polynomial f, denote by $P_f$ the number of integers n for which f(n) is a (positive) prime number. Let $q_d = max P_f$ , where f runs over all polynomials with integer coefficients with degree d and reducible over $\mathbb{Q}$ . Prove that $\forall d\geq 2$ , $q_d = d$ .