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