Factor $LaTeX: \displaystyle 3 x^{3} + 9 x^{2} + 24 x + 72$ .

Factoring out the GCF $LaTeX: \displaystyle 3$ from each term gives $LaTeX: \displaystyle 3(x^{3} + 3 x^{2} + 8 x + 24)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x + 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 8$ , gives $LaTeX: \displaystyle 8(x + 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x + 3$ . This gives $LaTeX: \displaystyle 3[x^{2} \left(x + 3\right) +8 \cdot \left(x + 3\right)] = 3\left(x + 3\right) \left(x^{2} + 8\right)$ .