Factor $LaTeX: \displaystyle - 15 x^{3} + 18 x^{2} - 40 x + 48$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(15 x^{3} - 18 x^{2} + 40 x - 48)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(5 x - 6)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 8$ , gives $LaTeX: \displaystyle 8(5 x - 6)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 5 x - 6$ . This gives $LaTeX: \displaystyle -1[3 x^{2} \left(5 x - 6\right) +8 \cdot \left(5 x - 6\right)] = -\left(5 x - 6\right) \left(3 x^{2} + 8\right)$ .