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n^{2}\left(7n+8\right)-6\left(7n+8\right)
Do the grouping 7n^{3}+8n^{2}-42n-48=\left(7n^{3}+8n^{2}\right)+\left(-42n-48\right), and factor out n^{2} in the first and -6 in the second group.
\left(7n+8\right)\left(n^{2}-6\right)
Factor out common term 7n+8 by using distributive property. Polynomial n^{2}-6 is not factored since it does not have any rational roots.