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3k^{2}\left(4k-5\right)-4\left(4k-5\right)
Do the grouping 12k^{3}-15k^{2}-16k+20=\left(12k^{3}-15k^{2}\right)+\left(-16k+20\right), and factor out 3k^{2} in the first and -4 in the second group.
\left(4k-5\right)\left(3k^{2}-4\right)
Factor out common term 4k-5 by using distributive property. Polynomial 3k^{2}-4 is not factored since it does not have any rational roots.