Factor $LaTeX: \displaystyle - 35 x^{3} + 45 x^{2} + 63 x - 81$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(35 x^{3} - 45 x^{2} - 63 x + 81)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 5 x^{2}$ , gives $LaTeX: \displaystyle 5 x^{2}(7 x - 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -9$ , gives $LaTeX: \displaystyle -9(7 x - 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 9$ . This gives $LaTeX: \displaystyle -1[5 x^{2} \left(7 x - 9\right) -9 \cdot \left(7 x - 9\right)] = -\left(7 x - 9\right) \left(5 x^{2} - 9\right)$ .