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x^{2}-5yx+6y^{2}+2y-4
Consider x^{2}-5xy+6y^{2}+2y-4 as a polynomial over variable x.
\left(x-2y-2\right)\left(x-3y+2\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor 6y^{2}+2y-4. One such factor is x-2y-2. Factor the polynomial by dividing it by this factor.