Answer
$x^2+3$
Work Step by Step
The given expression, $
(x^3-2x^2+3x-6)\div(x-2)
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^3-2x^2+3x-6}{x-2}
\\\\=
\dfrac{(x^3-2x^2)+(3x-6)}{x-2}
\\\\=
\dfrac{x^2(x-2)+3(x-2)}{x-2}
\\\\=
\dfrac{(x-2)(x^2+3)}{x-2}
\\\\=
\dfrac{(\cancel{x-2})(x^2+3)}{\cancel{x-2}}
\\\\=
x^2+3
.\end{array}
