Factor $LaTeX: \displaystyle 10 x^{3} - 5 x^{2} + 80 x - 40$ .

Factoring out the GCF $LaTeX: \displaystyle 5$ from each term gives $LaTeX: \displaystyle 5(2 x^{3} - x^{2} + 16 x - 8)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(2 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 8$ , gives $LaTeX: \displaystyle 8(2 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 2 x - 1$ . This gives $LaTeX: \displaystyle 5[x^{2} \left(2 x - 1\right) +8 \cdot \left(2 x - 1\right)] = 5\left(2 x - 1\right) \left(x^{2} + 8\right)$ .