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

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