Factor $LaTeX: \displaystyle 16 x^{3} - 80 x^{2} + 20 x - 100$ .

Factoring out the GCF $LaTeX: \displaystyle 4$ from each term gives $LaTeX: \displaystyle 4(4 x^{3} - 20 x^{2} + 5 x - 25)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 4 x^{2}$ , gives $LaTeX: \displaystyle 4 x^{2}(x - 5)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 5$ , gives $LaTeX: \displaystyle 5(x - 5)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle x - 5$ . This gives $LaTeX: \displaystyle 4[4 x^{2} \left(x - 5\right) +5 \cdot \left(x - 5\right)] = 4\left(x - 5\right) \left(4 x^{2} + 5\right)$ .