Factor $LaTeX: \displaystyle - 54 x^{3} - 90 x^{2} + 48 x + 80$ .

Factoring out the GCF $LaTeX: \displaystyle -2$ from each term gives $LaTeX: \displaystyle -2(27 x^{3} + 45 x^{2} - 24 x - 40)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 9 x^{2}$ , gives $LaTeX: \displaystyle 9 x^{2}(3 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -8$ , gives $LaTeX: \displaystyle -8(3 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 5$ . This gives $LaTeX: \displaystyle -2[9 x^{2} \left(3 x + 5\right) -8 \cdot \left(3 x + 5\right)] = -2\left(3 x + 5\right) \left(9 x^{2} - 8\right)$ .