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!

For a term of degree $d$,
$$2a_d(2x)^d=a_d(3x)^d+a_dx^d$$ requires
$$a_d(2^{d+1}-3^d-1)=0.$$
The only non-trivial solutions are with $d=0,d=1$, so that the polynomial is of the first degree.
