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2x^{2}+\left(-7y+7\right)x+6y^{2}-11y+3
Consider 2x^{2}-7xy+6y^{2}+7x-11y+3 as a polynomial over variable x.
\left(2x-3y+1\right)\left(x-2y+3\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 2x^{2} and n divides the constant factor 6y^{2}-11y+3. One such factor is 2x-3y+1. Factor the polynomial by dividing it by this factor.