Factor $LaTeX: \displaystyle - 35 x^{3} + 15 x^{2} + 56 x - 24$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(35 x^{3} - 15 x^{2} - 56 x + 24)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(7 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -8$ , gives $LaTeX: \displaystyle -8(7 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 3$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(7 x - 3\right) -8 \cdot \left(7 x - 3\right)] = -\left(7 x - 3\right) \left(5 x^{2} - 8\right)$ .