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

Factoring out the GCF $LaTeX: \displaystyle 10$ from each term gives $LaTeX: \displaystyle 10(3 x^{3} + 7 x^{2} - 3 x - 7)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(3 x + 7)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle -1$ , gives $LaTeX: \displaystyle -1(3 x + 7)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x + 7$ . This gives $LaTeX: \displaystyle 10[x^{2} \left(3 x + 7\right) -1 \cdot \left(3 x + 7\right)] = 10\left(3 x + 7\right) \left(x^{2} - 1\right)$ . The quadratic factor can be factored using the difference of squares to give $LaTeX: \displaystyle 10\left(x - 1\right) \left(x + 1\right) \left(3 x + 7\right).$