Let f(x) = 9x ^ 3 - 12x ^ 2 - 31 and let g(x) = 3x - 1 Find (f(x))/(g(x))

Question:
Solution:
Consider the following expression:
[tex]\frac{9x^3-12x^2-31}{3x-1}[/tex]Applying long division, this is equivalent to:
[tex]3x^2+\frac{-9x^2-31}{3x-1}[/tex]Finally, applying long division, this is equivalent to:
[tex]3x^2-3x-1-\frac{32}{3x-1}[/tex]So that, we can conclude that the correct answer is:
[tex]3x^2-3x-1-\frac{32}{3x-1}[/tex]