Factor $LaTeX: \displaystyle - 12 x^{3} - 18 x^{2} + 10 x + 15$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(12 x^{3} + 18 x^{2} - 10 x - 15)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 6 x^{2}$ , gives $LaTeX: \displaystyle 6 x^{2}(2 x + 3)$ . 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 $LaTeX: \displaystyle -1[6 x^{2} \left(2 x + 3\right) -5 \cdot \left(2 x + 3\right)] = -\left(2 x + 3\right) \left(6 x^{2} - 5\right)$ .