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