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6x^{2}+\left(19y-11\right)x+15y^{2}-17y+4
Consider 6x^{2}+19xy+15y^{2}-17y-11x+4 as a polynomial over variable x.
\left(2x+3y-1\right)\left(3x+5y-4\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 6x^{2} and n divides the constant factor 15y^{2}-17y+4. One such factor is 2x+3y-1. Factor the polynomial by dividing it by this factor.