Factor $LaTeX: \displaystyle 90 x^{3} + 60 x^{2} - 36 x - 24$ .

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