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