Let $P(x)=a_dx^d+....$ By setting $x=y=z$ in the given equation, $3P(x)+P(3x)=3P(2x)$ By comparing the leading coeffiecients of both sides we must have $3a_d+a_d \cdot 3^dx^d=a_d\cdot 3 \cdot 2^dx^d \implies 3^{d-1}=2^d-1$ So $d=1 or 2$ (otherwise for $d \geq 3$, $3^{d-1} > 2^d -1$) If $P(x)=ax+b$ putting this inti the given equation and simplyfying we get $b=0$ so $P(x)=ax$ for $a \in R$ If $P(x)$ is quadratic by plugging it in and simplyfying we will be left with $c=0$ so $P(x)=ax^2+bx$ for $a,b \in R$