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