Factor $LaTeX: \displaystyle - 35 x^{3} + 20 x^{2} - 21 x + 12$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(35 x^{3} - 20 x^{2} + 21 x - 12)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(7 x - 4)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(7 x - 4)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 4$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(7 x - 4\right) +3 \cdot \left(7 x - 4\right)] = -\left(7 x - 4\right) \left(5 x^{2} + 3\right)$ .