Factor $LaTeX: \displaystyle 3 x^{3} - 21 x^{2} - 10 x + 70$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 3 x^{2}$ , gives $LaTeX: \displaystyle 3 x^{2}(x - 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -10$ , gives $LaTeX: \displaystyle -10(x - 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 7$ . This gives $LaTeX: \displaystyle 3 x^{2} \left(x - 7\right) -10 \cdot \left(x - 7\right) = \left(x - 7\right) \left(3 x^{2} - 10\right)$ .