Factor $LaTeX: \displaystyle 12 x^{3} - 4 x^{2} + 48 x - 16$ .

Factoring out the GCF $LaTeX: \displaystyle 4$ from each term gives $LaTeX: \displaystyle 4(3 x^{3} - x^{2} + 12 x - 4)$ . Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle x^{2}$ , gives $LaTeX: \displaystyle x^{2}(3 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 4$ , gives $LaTeX: \displaystyle 4(3 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 3 x - 1$ . This gives $LaTeX: \displaystyle 4[x^{2} \left(3 x - 1\right) +4 \cdot \left(3 x - 1\right)] = 4\left(3 x - 1\right) \left(x^{2} + 4\right)$ .