Factor $LaTeX: \displaystyle - 21 x^{3} - 30 x^{2} + 35 x + 50$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(21 x^{3} + 30 x^{2} - 35 x - 50)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(7 x + 10)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -5$ , gives $LaTeX: \displaystyle -5(7 x + 10)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x + 10$ . This gives $LaTeX: \displaystyle -1[3 x^{2} \left(7 x + 10\right) -5 \cdot \left(7 x + 10\right)] = -\left(7 x + 10\right) \left(3 x^{2} - 5\right)$ .