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5p^{2}\left(p+1\right)-7\left(p+1\right)
Do the grouping 5p^{3}+5p^{2}-7p-7=\left(5p^{3}+5p^{2}\right)+\left(-7p-7\right), and factor out 5p^{2} in the first and -7 in the second group.
\left(p+1\right)\left(5p^{2}-7\right)
Factor out common term p+1 by using distributive property. Polynomial 5p^{2}-7 is not factored since it does not have any rational roots.