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5x^{2}\left(8x-5\right)+7\left(8x-5\right)
Do the grouping 40x^{3}-25x^{2}+56x-35=\left(40x^{3}-25x^{2}\right)+\left(56x-35\right), and factor out 5x^{2} in the first and 7 in the second group.
\left(8x-5\right)\left(5x^{2}+7\right)
Factor out common term 8x-5 by using distributive property. Polynomial 5x^{2}+7 is not factored since it does not have any rational roots.