Answer
$\displaystyle \frac{2x^{2}-5x-7}{x-2}=2x-1+\frac{-9}{x-2}$
Work Step by Step
Using synthetic division,
$ \left.\begin{array}{l}
2\lfloor \\ \\ \\ \end{array}\right. \begin{array}{rrr}
2 & -5 & -7\\\hline
& 4 & -2\\\hline
2 & -1 & -9
\end{array} $
$Q(x)=2x-1, \quad R(x)=-9$
In the form $\displaystyle \frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)}$,
$\displaystyle \frac{2x^{2}-5x-7}{x-2}=2x-1+\frac{-9}{x-2}$
