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y^{2}\left(5y+7\right)+6\left(5y+7\right)
Do the grouping 5y^{3}+7y^{2}+30y+42=\left(5y^{3}+7y^{2}\right)+\left(30y+42\right), and factor out y^{2} in the first and 6 in the second group.
\left(5y+7\right)\left(y^{2}+6\right)
Factor out common term 5y+7 by using distributive property. Polynomial y^{2}+6 is not factored since it does not have any rational roots.