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5v^{2}\left(5v+1\right)+6\left(5v+1\right)
Do the grouping 30v+5v^{2}+6+25v^{3}=\left(25v^{3}+5v^{2}\right)+\left(30v+6\right), and factor out 5v^{2} in the first and 6 in the second group.
\left(5v+1\right)\left(5v^{2}+6\right)
Factor out common term 5v+1 by using distributive property. Polynomial 5v^{2}+6 is not factored since it does not have any rational roots.