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