Let $P(x)$ be a nonconstant polynomial, where all the coefficients are nonnegative integers. Prove that there exist infinitely many positive

Let $P(x)$ be a nonconstant polynomial, where all the coefficients are nonnegative integers. Prove that there exist infinitely many positive integers $n$  such that $P(n)$ is composite.

This is obvious if you use the following fact: If m and n are integers, then m - n divides P(m) - P(n).