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7x^{2}\left(7x-5\right)+8\left(7x-5\right)
Do the grouping 49x^{3}-35x^{2}+56x-40=\left(49x^{3}-35x^{2}\right)+\left(56x-40\right), and factor out 7x^{2} in the first and 8 in the second group.
\left(7x-5\right)\left(7x^{2}+8\right)
Factor out common term 7x-5 by using distributive property. Polynomial 7x^{2}+8 is not factored since it does not have any rational roots.