AZ-MO 2015 Problem 3

Find all polynomials $P(x)$ with real coefficents such that $P(P(x))=(x^2+x+1)\cdot P(x)$ where $x \in \mathbb{R}$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.