UA-UMO 2023 Problem 106

Let $P(x), Q(x), R(x)$ be polynomials with integer coefficients, such that $P(x) = Q(x)R(x)$ . Let's denote by $a$ and $b$ the largest absolute values of coefficients of $P, Q$ correspondingly. Does $b \le 2023a$ always hold?

Proposed by Dmytro Petrovsky