Factor $LaTeX: \displaystyle 2 x^{3} + 4 x^{2} - 12 x - 24$ .

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