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