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

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