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