Answer
Quotient $=3x^2-7x+15$
Remainder $=-32$
Work Step by Step
The given expression is
$(3x^3-x^2+x-2)\div(x+2)$
Perform long division to obtain:
$\begin{matrix}
& 3x^2 & -7x &+15 & & \leftarrow &\text{ Quotient}\\
&-- &-- &--&--& \\
x+2) &3x^3&-x^2&+x&-2 & \\
& 3x^3 & +6x^2 & & & \leftarrow &3x^2(x+2) \\
& -- & -- & & & \leftarrow &\text{ subtract} \\
& 0 & -7x^2 & +x & & \\
& & -7x^2 & -14x & & \leftarrow & -7x(x+2) \\
& & -- & -- & & \leftarrow & \text{ subtract} \\
& & 0&15x &-2 & \\
& & & 15x& +30 & \leftarrow & 15(x+2) \\
& & & -- & -- & \leftarrow & \text{ subtract} \\
& & & 0 & -32 & \leftarrow & \text{ Remainder}
\end{matrix}$
Checking:
(Quotient)(divisor)+ Remainder
$=(3x^2-7x+15)(x+2)-32$
$=3x^3-7x^2+15x+6x^2-14x+30-32$
$=3x^3-x^2+x-2$
$=$ Dividend
Hence, the Quotient is $3x^2-7x+15$.
and the remainder is $-32$.
