Question 4
Find all polynomials $P(x)$ with real coefficients that satisfy the equality
$$ P(a-b)+P(b-c)+P(c-a)=2P(a+b+c) $$
for all triples $a, b, c$ of real numbers such that $ab + bc + ca = 0$.
$$ P(a-b)+P(b-c)+P(c-a)=2P(a+b+c) $$
for all triples $a, b, c$ of real numbers such that $ab + bc + ca = 0$.