Factor $LaTeX: \displaystyle 56 x^{3} + 70 x^{2} - 32 x - 40$ .

Factoring out the GCF $LaTeX: \displaystyle 2$ from each term gives $LaTeX: \displaystyle 2(28 x^{3} + 35 x^{2} - 16 x - 20)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 7 x^{2}$ , gives $LaTeX: \displaystyle 7 x^{2}(4 x + 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(4 x + 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x + 5$ . This gives $LaTeX: \displaystyle 2[7 x^{2} \left(4 x + 5\right) -4 \cdot \left(4 x + 5\right)] = 2\left(4 x + 5\right) \left(7 x^{2} - 4\right)$ .