When does the product of two polynomials = $x^{k}$? Suppose $f$ and $g$ are are two polynomials with complex coefficents (i.e $f,g \in \mathbb{C}[x]$).
Let $m$ be the order of $f$ and let $n$ be the order of $g$.
Are there some general conditions where  
$fg= \alpha x^{n+m}$
for some non-zero $\alpha \in \mathbb{C}$ 

The answer just occured to me.   The roots of $f$ and $g$ must be be at 0. 
