Find the oblique (slant) asymptote of $LaTeX: \displaystyle f(x) = \frac{x^{3} + 7 x^{2} - 80 x - 576}{x^{2} + 14 x + 45}$ .

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

Dividing gives the quotient $LaTeX: \displaystyle x - 7$ and the remainder $LaTeX: \displaystyle - 27 x - 261$ . The oblique asymptote is $LaTeX: \displaystyle y = x - 7$ .