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x^{2}\left(x+2\right)+7\left(x+2\right)
Do the grouping x^{3}+2x^{2}+7x+14=\left(x^{3}+2x^{2}\right)+\left(7x+14\right), and factor out x^{2} in the first and 7 in the second group.
\left(x+2\right)\left(x^{2}+7\right)
Factor out common term x+2 by using distributive property. Polynomial x^{2}+7 is not factored since it does not have any rational roots.