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3x^{2}\left(x+4\right)-7\left(x+4\right)
Do the grouping 3x^{3}+12x^{2}-7x-28=\left(3x^{3}+12x^{2}\right)+\left(-7x-28\right), and factor out 3x^{2} in the first and -7 in the second group.
\left(x+4\right)\left(3x^{2}-7\right)
Factor out common term x+4 by using distributive property. Polynomial 3x^{2}-7 is not factored since it does not have any rational roots.