Factor $LaTeX: \displaystyle 8 x^{3} - 20 x^{2} - 32 x + 80$ .

Factoring out the GCF $LaTeX: \displaystyle 4$ from each term gives $LaTeX: \displaystyle 4(2 x^{3} - 5 x^{2} - 8 x + 20)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(2 x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -4$ , gives $LaTeX: \displaystyle -4(2 x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 5$ . This gives $LaTeX: \displaystyle 4[x^{2} \left(2 x - 5\right) -4 \cdot \left(2 x - 5\right)] = 4\left(2 x - 5\right) \left(x^{2} - 4\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle 4\left(x - 2\right) \left(x + 2\right) \left(2 x - 5\right).$