Factor $LaTeX: \displaystyle - 50 x^{3} + 15 x^{2} - 70 x + 21$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(50 x^{3} - 15 x^{2} + 70 x - 21)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(10 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 7$ , gives $LaTeX: \displaystyle 7(10 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 10 x - 3$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(10 x - 3\right) +7 \cdot \left(10 x - 3\right)] = -\left(10 x - 3\right) \left(5 x^{2} + 7\right)$ .