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