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v^{2}+12yv+11y^{2}
Consider v^{2}+12vy+11y^{2} as a polynomial over variable v.
\left(11y+v\right)\left(y+v\right)
Find one factor of the form v^{k}+m, where v^{k} divides the monomial with the highest power v^{2} and m divides the constant factor 11y^{2}. One such factor is 11y+v. Factor the polynomial by dividing it by this factor.