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4x^{2}+2x-9y^{2}+3y
Consider 4x^{2}+2x-9y^{2}+3y as a polynomial over variable x.
\left(2x+3y\right)\left(2x-3y+1\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}+3y. One such factor is 2x+3y. Factor the polynomial by dividing it by this factor.