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x^{2}\left(6x+7\right)+7\left(6x+7\right)
Do the grouping 6x^{3}+7x^{2}+42x+49=\left(6x^{3}+7x^{2}\right)+\left(42x+49\right), and factor out x^{2} in the first and 7 in the second group.
\left(6x+7\right)\left(x^{2}+7\right)
Factor out common term 6x+7 by using distributive property. Polynomial x^{2}+7 is not factored since it does not have any rational roots.