Factor $LaTeX: \displaystyle 24 x^{3} + 30 x^{2} - 72 x - 90$ .

Factoring out the GCF $LaTeX: \displaystyle 6$ from each term gives $LaTeX: \displaystyle 6(4 x^{3} + 5 x^{2} - 12 x - 15)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(4 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -3$ , gives $LaTeX: \displaystyle -3(4 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x + 5$ . This gives $LaTeX: \displaystyle 6[x^{2} \left(4 x + 5\right) -3 \cdot \left(4 x + 5\right)] = 6\left(4 x + 5\right) \left(x^{2} - 3\right)$ .