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