Factor $LaTeX: \displaystyle - 21 x^{3} - 15 x^{2} - 7 x - 5$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(21 x^{3} + 15 x^{2} + 7 x + 5)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(7 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(7 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x + 5$ . This gives $LaTeX: \displaystyle -1[3 x^{2} \left(7 x + 5\right) +1 \cdot \left(7 x + 5\right)] = -\left(7 x + 5\right) \left(3 x^{2} + 1\right)$ .