Factor $LaTeX: \displaystyle - 10 x^{3} - 9 x^{2} + 70 x + 63$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(10 x^{3} + 9 x^{2} - 70 x - 63)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(10 x + 9)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -7$ , gives $LaTeX: \displaystyle -7(10 x + 9)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 10 x + 9$ . This gives $LaTeX: \displaystyle -1[x^{2} \left(10 x + 9\right) -7 \cdot \left(10 x + 9\right)] = -\left(10 x + 9\right) \left(x^{2} - 7\right)$ .