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