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u^{2}-vu-6v^{2}
Consider u^{2}-uv-6v^{2} as a polynomial over variable u.
\left(u-3v\right)\left(u+2v\right)
Find one factor of the form u^{k}+m, where u^{k} divides the monomial with the highest power u^{2} and m divides the constant factor -6v^{2}. One such factor is u-3v. Factor the polynomial by dividing it by this factor.