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x^{2}+\left(2y+4\right)x-3y^{2}-8y-5
Consider x^{2}-3y^{2}+2xy+4x-8y-5 as a polynomial over variable x.
\left(x-y-1\right)\left(x+3y+5\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{2} and m divides the constant factor -3y^{2}-8y-5. One such factor is x-y-1. Factor the polynomial by dividing it by this factor.