Quadratic Functional equations. Suppose $f$ is a quadratic ploynomial, with leading cofficient $1$, such that $$f(f(x) +x) = f(x)(x^2+786x+439)$$ For all real number $x$. What is the value of $f(3)$?

Stupid method: 
Let $f(x) = x^2 + ax + b$. Then the left hand side of the equation is 
$$\begin{split}
f(f(x) + x) & =f( x^2 + ax + b + x) \\
&= (x^2+ (a+1)x +b)^2 + a(x^2+(a+1) x+ b) + b
\end{split}$$
If you compare the $x^3$ coefficient, this gives $2(a+1) = 786 +a$. Comparing the constant coefficient tells you $b$. 
