Question 147
Find all polynomials $P$ with real coefficients such that
$$
P(x)P(x+1) = P(x^2 - x + 3) \quad \forall x \in \mathbb{R},
$$
where $\mathbb{R}$ denotes the set of all real numbers.
$$
P(x)P(x+1) = P(x^2 - x + 3) \quad \forall x \in \mathbb{R},
$$
where $\mathbb{R}$ denotes the set of all real numbers.