Factor $LaTeX: \displaystyle - 12 x^{3} - 8 x^{2} + 30 x + 20$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(6 x^{3} + 4 x^{2} - 15 x - 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(3 x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(3 x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 2$ . This gives $LaTeX: \displaystyle -2[2 x^{2} \left(3 x + 2\right) -5 \cdot \left(3 x + 2\right)] = -2\left(3 x + 2\right) \left(2 x^{2} - 5\right)$ .