Nemotron-IMO-Bench 2026 A29

Let $P\in \mathbb{Q}[X]$ be a nonconstant irreducible polynomial of degree $n$. Prove that there are at most $n$ polynomials $Q\in \mathbb{Q}[X]$ of degree less than $n$ such that $P(X)$ divides $P(Q(X))$.