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2n^{2}\left(7n+2\right)-7\left(7n+2\right)
Do the grouping 14n^{3}+4n^{2}-49n-14=\left(14n^{3}+4n^{2}\right)+\left(-49n-14\right), and factor out 2n^{2} in the first and -7 in the second group.
\left(7n+2\right)\left(2n^{2}-7\right)
Factor out common term 7n+2 by using distributive property. Polynomial 2n^{2}-7 is not factored since it does not have any rational roots.