Factor $LaTeX: \displaystyle 40 x^{3} + 30 x^{2} - 72 x - 54$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(20 x^{3} + 15 x^{2} - 36 x - 27)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(4 x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -9$ , gives $LaTeX: \displaystyle -9(4 x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x + 3$ . This gives $LaTeX: \displaystyle 2[5 x^{2} \left(4 x + 3\right) -9 \cdot \left(4 x + 3\right)] = 2\left(4 x + 3\right) \left(5 x^{2} - 9\right)$ .