Factor $LaTeX: \displaystyle - 10 x^{3} - 6 x^{2} + 40 x + 24$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(5 x^{3} + 3 x^{2} - 20 x - 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(5 x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(5 x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x + 3$ . This gives $LaTeX: \displaystyle -2[x^{2} \left(5 x + 3\right) -4 \cdot \left(5 x + 3\right)] = -2\left(5 x + 3\right) \left(x^{2} - 4\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle -2\left(x - 2\right) \left(x + 2\right) \left(5 x + 3\right).$