What skill do I lack to factor multivariate polynomials? Ok so I can factor easily regular quadratic polynomials, i.e. $5x^2+7x+9$ (I'm not sure whether that's prime, just made it up), and I was working on solving $y^2+(x^2+2x−2)y+(x^3−x^2−2x)$ by distributing the $y$ after the first parentheses and now I'm stuck. Am I just missing some skill in factoring multivariate polynomials? Don't tell me stuff about rings and fields because that won't help my situation. Thanks

Comment on previous answers, with $A=1,$ $B = x^2 + 2x-2,$ $C = x^3 - x^2 -2x$ we get
$$  B^2 - 4 AC = x^4 + 4 x^2 + 4 = (x^2 + 2)^2,  $$ so, in the quadratic formula, $\sqrt {B^2 - 4AC} = x^2 + 2.$ The "roots" for $y$ are
$$  \frac{-B \pm \sqrt {B^2 - 4AC}}{2A}, $$ so the factors are
$$ \left( y -  \frac{-B - \sqrt {B^2 - 4AC}}{2A} \right)  \left( y -  \frac{-B + \sqrt {B^2 - 4AC}}{2A} \right),   $$
$$ \left( y +  \frac{B + \sqrt {B^2 - 4AC}}{2A} \right)  \left( y +  \frac{B - \sqrt {B^2 - 4AC}}{2A} \right),   $$
$$ \left( y +  \frac{x^2 + 2 x - 2 + x^2 + 2}{2} \right)  \left( y +  \frac{x^2 + 2 x - 2 - x^2 - 2}{2} \right),   $$
$$ \left( y +  \frac{2x^2 + 2 x }{2} \right)  \left( y +  \frac{ 2 x - 4 }{2} \right),   $$
$$ \left( y +  x^2 + x \right)  \left( y +  x-2 \right).  $$
