<s>[INST] Can we factor multivariate polynomial $x+xy+y$? It seems to me we can only get $x(1+y)+y$ or $x+(x+1)y$, but maybe something better is possible with complex numbers?
It has zeros at $y=-\frac{x}{x+1}$, but how to use that fact?
 [/INST] A possible factorization is :
$\begin{align}x+xy+y &=x+xy+y+1-1\\ &=x(y+1)+(y+1)-1 \\ &=(x+1)(y+1)-1 \\ &=\left(\sqrt{(x+1)(y+1)}\right)^2-1^2 ,\text{assuming $x,y \gt -1$} \\ &=\left(\sqrt{(x+1)(y+1)}+1\right)\cdot\left(\sqrt{(x+1)(y+1)}-1\right)\end{align}$
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