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4x^{2}\left(4x+3\right)+3\left(4x+3\right)
Do the grouping 16x^{3}+12x^{2}+12x+9=\left(16x^{3}+12x^{2}\right)+\left(12x+9\right), and factor out 4x^{2} in the first and 3 in the second group.
\left(4x+3\right)\left(4x^{2}+3\right)
Factor out common term 4x+3 by using distributive property. Polynomial 4x^{2}+3 is not factored since it does not have any rational roots.