Answer
$2x^2+\dfrac{1}{2}x-5$
Work Step by Step
Using the long division below, then
\begin{array}{l}\require{cancel}\left(
2x^3+\dfrac{9}{2}x^2-4x-10
\right)\div(
x+2
)\\\\=
2x^2+\dfrac{1}{2}x-5
.\end{array}
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