<s>[INST] Factoring High School Level Olympiad Problem Factor $x^2 - 3xy + 2y^2 + x -8y - 6$
Attempt at a solution:
I have factored these and don't know how to continue...
$x^2-3xy +2y^2 = (x - y) (x-2y)$
$x^2 + x -6 = (x + 3) (x - 2)$
$2y^2 - 8y + 6 = 2 (y - 3)(y - 1)$ 
 [/INST] Look for in form:
$$x^2-3xy+2y^2+x-8y-6=(x+Ay+B)(x+Cy+D)
$$
Plug $y=0$:
$$x^2+x-6=(x+B)(x+D) \Rightarrow B=3; D=-2.$$
Plug $x=0$:
$$2y^2-8y-6=(Ay+3)(Cy-2) \Rightarrow \begin{cases} AC=2 \\ -2A+3C=-8 \end{cases}$$
Can you finish?
Appendix: Note that the found parameters will not be suitable. So this method may not always work.
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