Factor $LaTeX: \displaystyle - x^{3} + 10 x^{2} - 5 x + 50$ .

Factoring out the GCF $LaTeX: \displaystyle -1$ from each term gives $LaTeX: \displaystyle -(x^{3} - 10 x^{2} + 5 x - 50)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(x - 10)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 5$ , gives $LaTeX: \displaystyle 5(x - 10)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 10$ . This gives $LaTeX: \displaystyle -1[x^{2} \left(x - 10\right) +5 \cdot \left(x - 10\right)] = -\left(x - 10\right) \left(x^{2} + 5\right)$ .