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v^{2}\left(5v-6\right)-5\left(5v-6\right)
Do the grouping 5v^{3}-6v^{2}-25v+30=\left(5v^{3}-6v^{2}\right)+\left(-25v+30\right), and factor out v^{2} in the first and -5 in the second group.
\left(5v-6\right)\left(v^{2}-5\right)
Factor out common term 5v-6 by using distributive property. Polynomial v^{2}-5 is not factored since it does not have any rational roots.