Answer
The sum is, $a+b+c+d=1-4+11-17=-9$.
Work Step by Step
$\begin{array}{lllllll}
& & x^{2} & -4x & +11 & \\
& -- & -- & -- & -- & -- & \\
x+2\ ) & x^{3} & -2x^{2} & +3x & +5 & \\
& -x^{3} & -2x^{2} & & & & \\
& -- & -- & & & & \\
& & -4x^{2} & +3x & & & \\
& & 4x^{2} & +8x & & & \\
& & -- & -- & & & \\
& & & 11x & +5 & & \\
& & & -11x & -22 & & \\
& & & -- & -- & & \\
& & & & -17 & \\
\end{array}$
$x^{3}-2x^{2}+3x+5=x^{2}-4x+11-\frac{17}{x+2}$
Thus, $a=1, b=-4, c=11, d=-17$.
The sum is, $a+b+c+d=1-4+11-17=-9$.
