Factor $LaTeX: \displaystyle 50 x^{3} - 50 x^{2} + 15 x - 15$ .

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