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6v^{2}x^{2}-23vx+21
Consider 6x^{2}v^{2}-23xv+21 as a polynomial over variable x.
\left(2vx-3\right)\left(3vx-7\right)
Find one factor of the form kv^{m}x^{n}+p, where kv^{m}x^{n} divides the monomial with the highest power 6v^{2}x^{2} and p divides the constant factor 21. One such factor is 2vx-3. Factor the polynomial by dividing it by this factor.