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x^{2}+\left(-5y+6\right)x+6y^{2}-13y+5
Consider x^{2}-5xy+6y^{2}+6x-13y+5 as a polynomial over variable x.
\left(x-3y+5\right)\left(x-2y+1\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}-13y+5. One such factor is x-3y+5. Factor the polynomial by dividing it by this factor.