Factor $LaTeX: \displaystyle 3 x^{3} - 5 x^{2} + 30 x - 50$ .

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