Factor $LaTeX: \displaystyle - 6 x^{3} - x^{2} - 24 x - 4$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(6 x^{3} + x^{2} + 24 x + 4)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(6 x + 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 4$ , gives $LaTeX: \displaystyle 4(6 x + 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 6 x + 1$ . This gives $LaTeX: \displaystyle -1[x^{2} \left(6 x + 1\right) +4 \cdot \left(6 x + 1\right)] = -\left(6 x + 1\right) \left(x^{2} + 4\right)$ .