Answer
Quotient $=3x-1$
Remainder $=x-2$
Work Step by Step
The given expression is
$(3x^3-x^2+x-2)\div(x^2)$
Perform long division to obtain:
$\begin{matrix}
& 3x & -1 & & & \leftarrow &\text{Quotient}\\
&-- &-- &--&--& \\
x^2) &3x^3&-x^2&+x&-2 & \\
& 3x^3 & & & & \leftarrow &3x(x^2) \\
& -- & -- & & & \leftarrow &\text{subtract} \\
& 0 & -x^2 & & & \\
& & -x^2 & & & \leftarrow & -1(x^2) \\
& & -- & -- & & \leftarrow & \text{subtract} \\
& & 0&x &-2& \leftarrow & \text{Remainder}
\end{matrix}$
Checking:
(Quotient)(divisor)+ Remainder
$=(3x-1)(x^2)+x-2$
$=3x^3-x^2+x-2$
$=$ Dividend
Hence, the Quotient is $3x-1$ and the remainder is $x-2$.
