Find the oblique (slant) asymptote of $LaTeX: \displaystyle f(x) = \frac{x^{3} - 15 x^{2} + 27 x + 243}{x^{2} - x - 30}$ .

The oblique asymptote is the whole part without the remainder after polynomial long division.

Dividing gives the quotient $LaTeX: \displaystyle x - 14$ and the remainder $LaTeX: \displaystyle 43 x - 177$ . The oblique asymptote is $LaTeX: \displaystyle y = x - 14$ .