Factor $LaTeX: \displaystyle 35 x^{3} - 15 x^{2} + 70 x - 30$ .

Factoring out the GCF $LaTeX: \displaystyle 5$ from each term gives $LaTeX: \displaystyle 5(7 x^{3} - 3 x^{2} + 14 x - 6)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(7 x - 3)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 2$ , gives $LaTeX: \displaystyle 2(7 x - 3)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 7 x - 3$ . This gives $LaTeX: \displaystyle 5[x^{2} \left(7 x - 3\right) +2 \cdot \left(7 x - 3\right)] = 5\left(7 x - 3\right) \left(x^{2} + 2\right)$ .