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v^{2}\left(5v+3\right)-2\left(5v+3\right)
Do the grouping 5v^{3}+3v^{2}-10v-6=\left(5v^{3}+3v^{2}\right)+\left(-10v-6\right), and factor out v^{2} in the first and -2 in the second group.
\left(5v+3\right)\left(v^{2}-2\right)
Factor out common term 5v+3 by using distributive property. Polynomial v^{2}-2 is not factored since it does not have any rational roots.