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

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