Factor $LaTeX: \displaystyle 50 x^{3} - 15 x^{2} + 10 x - 3$ .

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