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2x^{2}\left(6x+1\right)-5\left(6x+1\right)
Do the grouping 12x^{3}+2x^{2}-30x-5=\left(12x^{3}+2x^{2}\right)+\left(-30x-5\right), and factor out 2x^{2} in the first and -5 in the second group.
\left(6x+1\right)\left(2x^{2}-5\right)
Factor out common term 6x+1 by using distributive property. Polynomial 2x^{2}-5 is not factored since it does not have any rational roots.