Problem

Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade

Tags: algebra, Polynomials



Find all polynomials $P,Q\in \mathbb{R}[x]$, such that $P(2)=2$ , $Q(x)$ has no negative roots, and $(x-2)P(x^2-1)Q(x+1)=P(x)Q(x^2 )+Q(x+1)$.