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4x^{2}+\left(12y-8\right)x+9y^{2}-12y
Consider 4x^{2}+12xy+9y^{2}-8x-12y as a polynomial over variable x.
\left(2x+3y\right)\left(2x+3y-4\right)
Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 4x^{2} and n divides the constant factor 9y^{2}-12y. One such factor is 2x+3y. Factor the polynomial by dividing it by this factor.