Find all Polynomials P(x) with real coefficients Find all Polynomials P(x) with real coefficients so that $2P(2x) = P(3x) + P(x)$.
I tried to substitute first degree, second and third, bit couldn't get an equality. Thank you for your responses!

Let the polynomial be $a_nx^n+\dots+ a_0$
then the leading term of the polynomial on the left is $2^{n+1}a_n$ and the leading term of the polynomial on the right is $(3^n+1)a_n$
So clearly we must have $n=1$ or $0$.
So the polynomial is of the form $ax+b$. and any of these work as we have:
$4ax+2b=3ax+b+ax+b$
