Solve {l}{x^2-2y^2}{-z^2}{+3yz-xy}

$$\left. \begin{array} { l } { x ^ { 2 } - 2 y ^ { 2 } } \\ { - z ^ { 2 } } \\ { + 3 y z - x y } \end{array} \right.$$

Factor

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

Solution Steps

Consider x^{2}-2y^{2}-z^{2}+3yz-xy as a polynomial over variable x.

$$x^{2}-yx-2y^{2}-z^{2}+3yz$$

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}+3yz-z^{2}. One such factor is x+y-z. Factor the polynomial by dividing it by this factor.

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

Evaluate

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