Factor $LaTeX: \displaystyle 40 x^{3} - 10 x^{2} + 12 x - 3$ .

Grouping the first two terms and factoring out their GCF, $LaTeX: \displaystyle 10 x^{2}$ , gives $LaTeX: \displaystyle 10 x^{2}(4 x - 1)$ . Grouping the last two terms and factoring out their GCF, $LaTeX: \displaystyle 3$ , gives $LaTeX: \displaystyle 3(4 x - 1)$ . The polynomial now has a common binomial factor of $LaTeX: \displaystyle 4 x - 1$ . This gives $LaTeX: \displaystyle 10 x^{2} \left(4 x - 1\right) +3 \cdot \left(4 x - 1\right) = \left(4 x - 1\right) \left(10 x^{2} + 3\right)$ .