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3r^{2}\left(3r+2\right)+2\left(3r+2\right)
Do the grouping 9r^{3}+6r^{2}+6r+4=\left(9r^{3}+6r^{2}\right)+\left(6r+4\right), and factor out 3r^{2} in the first and 2 in the second group.
\left(3r+2\right)\left(3r^{2}+2\right)
Factor out common term 3r+2 by using distributive property. Polynomial 3r^{2}+2 is not factored since it does not have any rational roots.