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x^{2}+\left(-2y-5\right)x+y^{2}+5y-6
Consider x^{2}-2xy+y^{2}-5x+5y-6 as a polynomial over variable x.
\left(x-y+1\right)\left(x-y-6\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 y^{2}+5y-6. One such factor is x-y+1. Factor the polynomial by dividing it by this factor.