Factor $LaTeX: \displaystyle 6 x^{3} - 8 x^{2} - 18 x + 24$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(3 x^{3} - 4 x^{2} - 9 x + 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(3 x - 4)$ . 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 $LaTeX: \displaystyle 2[x^{2} \left(3 x - 4\right) -3 \cdot \left(3 x - 4\right)] = 2\left(3 x - 4\right) \left(x^{2} - 3\right)$ .