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x^{2}\left(x+3\right)-2\left(x+3\right)
Do the grouping x^{3}+3x^{2}-2x-6=\left(x^{3}+3x^{2}\right)+\left(-2x-6\right), and factor out x^{2} in the first and -2 in the second group.
\left(x+3\right)\left(x^{2}-2\right)
Factor out common term x+3 by using distributive property. Polynomial x^{2}-2 is not factored since it does not have any rational roots.