Factor $LaTeX: \displaystyle 24 x^{3} + 48 x^{2} + 30 x + 60$ .

Factoring out the GCF $LaTeX: \displaystyle 6$ from each term gives $LaTeX: \displaystyle 6(4 x^{3} + 8 x^{2} + 5 x + 10)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(x + 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 5$ , gives $LaTeX: \displaystyle 5(x + 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 2$ . This gives $LaTeX: \displaystyle 6[4 x^{2} \left(x + 2\right) +5 \cdot \left(x + 2\right)] = 6\left(x + 2\right) \left(4 x^{2} + 5\right)$ .