Factor $LaTeX: \displaystyle 7 x^{3} - 2 x^{2} - 35 x + 10$ .

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