Factor $LaTeX: \displaystyle 60 x^{3} + 80 x^{2} + 18 x + 24$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(30 x^{3} + 40 x^{2} + 9 x + 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 10 x^{2}$ , gives $LaTeX: \displaystyle 10 x^{2}(3 x + 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(3 x + 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 4$ . This gives $LaTeX: \displaystyle 2[10 x^{2} \left(3 x + 4\right) +3 \cdot \left(3 x + 4\right)] = 2\left(3 x + 4\right) \left(10 x^{2} + 3\right)$ .