VN-TST 1992 Problem 2

Let a polynomial $f(x)$ be given with real coefficients and has degree greater or equal than 1. Show that for every real number $c > 0$ , there exists a positive integer $n_0$ satisfying the following condition: if polynomial $P(x)$ of degree greater or equal than $n_0$ with real coefficients and has leading coefficient equal to 1 then the number of integers $x$ for which $|f(P(x))| \leq c$ is not greater than degree of $P(x)$ .