Question

How can I use synthetic division if there's not a linear function in the denominator? (-2x^2+7x+15) / (2x-9)

Answer 1

I'm trying to find the oblique asymptote by the way.

Answer 2

\(2x-9\) IS a linear function.

Answer 3

To be able to set up synthetic division, however, you have to have the coefficient of the leading term be 1.
\[\frac{-2x^2+7x+15}{2x-9}=\frac{-x^2+\dfrac{7}{2}x+\dfrac{15}{2}}{x-\dfrac{9}{2}}\]