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2x^{2}+\left(8y+11\right)x+6y^{2}+13y+5
Consider 2x^{2}+8xy+6y^{2}+11x+13y+5 as a polynomial over variable x.
\left(2x+2y+1\right)\left(x+3y+5\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}+13y+5. One such factor is 2x+2y+1. Factor the polynomial by dividing it by this factor.