<s>[INST] Find all polynomials $Q(x)(x^2-6x+8) =Q(x-2)(x^2-6x)$ for $x\in \Bbb R$ 
Find all polynomials $Q(x)(x^2-6x+8) =Q(x-2)(x^2-6x)$ for $x\in \Bbb R$

I've tried different substitutions like put $Q(x)$ $=$ $k$ for some $k$ and getting the equation $k(x^2-6x+8)$ $=$ $(k-2)(x^2-6x)$ $<=>$ $k$=$(6x-x^2)/4$, but that doesn't give equlity. Thank you for your help
 [/INST] maybe Hint:Some information come out from $Q(x)(x^2-6x+8) =Q(x-2)(x^2-6x)$
$$x=0 \to Q(0)(8)=Q(-2)0 \to Q(0)=0\\
x=6 \to Q(6)(8)=Q(6-2)0 \to Q(6)=0\\
x=4 \to Q(4)(0)=Q(2)(16-24) \to Q(4)=0$$ so $Q(x)$ at least  contain $$Q(x)=(x-0)(x-4)(x-6)$$ or 
$$Q(x)=(x-0)(x-6)(x-4)q(x)$$
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