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2n^{2}\left(5n-2\right)-7\left(5n-2\right)
Do the grouping 10n^{3}-4n^{2}-35n+14=\left(10n^{3}-4n^{2}\right)+\left(-35n+14\right), and factor out 2n^{2} in the first and -7 in the second group.
\left(5n-2\right)\left(2n^{2}-7\right)
Factor out common term 5n-2 by using distributive property. Polynomial 2n^{2}-7 is not factored since it does not have any rational roots.