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y^{2}+\left(6z-3\right)y+9z^{2}-9z
Consider y^{2}+6yz+9z^{2}-3y-9z as a polynomial over variable y.
\left(y+3z\right)\left(y+3z-3\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 9z^{2}-9z. One such factor is y+3z. Factor the polynomial by dividing it by this factor.