Solve x^2+xy-2y^2-x+7y-6

$$x ^ { 2 } + x y - 2 y ^ { 2 } - x + 7 y - 6$$

Factor

$$\left(x-y+2\right)\left(x+2y-3\right)$$

Solution Steps

Consider x^{2}+xy-2y^{2}-x+7y-6 as a polynomial over variable x.

$$x^{2}+\left(y-1\right)x-2y^{2}+7y-6$$

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 -2y^{2}+7y-6. One such factor is x-y+2. Factor the polynomial by dividing it by this factor.

$$\left(x-y+2\right)\left(x+2y-3\right)$$

Evaluate

$$\left(x-y+2\right)\left(x+2y-3\right)$$