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

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