Factor LaTeX: \displaystyle - 5 x^{3} + 3 x^{2} + 45 x - 27 .

Factoring out the GCF LaTeX: \displaystyle -1 from each term gives LaTeX: \displaystyle -(5 x^{3} - 3 x^{2} - 45 x + 27) . Grouping the first two terms and factoring out their GCF, LaTeX: \displaystyle x^{2} , gives LaTeX: \displaystyle x^{2}(5 x - 3) . Grouping the last two terms and factoring out their GCF, LaTeX: \displaystyle -9 , gives LaTeX: \displaystyle -9(5 x - 3) . The polynomial now has a common binomial factor of LaTeX: \displaystyle 5 x - 3 . This gives LaTeX: \displaystyle -1[x^{2} \left(5 x - 3\right) -9 \cdot \left(5 x - 3\right)] = -\left(5 x - 3\right) \left(x^{2} - 9\right) . The quadratic factor can be factored using the difference of squares to give LaTeX: \displaystyle -\left(x - 3\right) \left(x + 3\right) \left(5 x - 3\right).