Factor $LaTeX: \displaystyle 7 x^{3} - 35 x^{2} - 8 x + 40$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 7 x^{2}$ , gives $LaTeX: \displaystyle 7 x^{2}(x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -8$ , gives $LaTeX: \displaystyle -8(x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 5$ . This gives $LaTeX: \displaystyle 7 x^{2} \left(x - 5\right) -8 \cdot \left(x - 5\right) = \left(x - 5\right) \left(7 x^{2} - 8\right)$ .