Question 18
Find all polynomials $P$ with real coefficients such that for all $x, y, z \in \mathbb{R}$,
$$
P(x) + P(y) + P(z) + P(x + y + z) = P(x + y) + P(y + z) + P(z + x).
$$
$$
P(x) + P(y) + P(z) + P(x + y + z) = P(x + y) + P(y + z) + P(z + x).
$$