Factor $LaTeX: \displaystyle - 15 x^{3} + 40 x^{2} - 21 x + 56$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(15 x^{3} - 40 x^{2} + 21 x - 56)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(3 x - 8)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 7$ , gives $LaTeX: \displaystyle 7(3 x - 8)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x - 8$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(3 x - 8\right) +7 \cdot \left(3 x - 8\right)] = -\left(3 x - 8\right) \left(5 x^{2} + 7\right)$ .