Factor $LaTeX: \displaystyle - 10 x^{3} + 20 x^{2} - 5 x + 10$ .

Factoring out the GCF $LaTeX: \displaystyle -5$ from each term gives $LaTeX: \displaystyle -5(2 x^{3} - 4 x^{2} + x - 2)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 2 x^{2}$ , gives $LaTeX: \displaystyle 2 x^{2}(x - 2)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 1$ , gives $LaTeX: \displaystyle 1(x - 2)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 2$ . This gives $LaTeX: \displaystyle -5[2 x^{2} \left(x - 2\right) +1 \cdot \left(x - 2\right)] = -5\left(x - 2\right) \left(2 x^{2} + 1\right)$ .