Answer
$3x^2 -3x+1+\frac{2}{3x+2}$.
Work Step by Step
Divide the polynomial $9x^3-3x^2-3x+4$ by $3x+2$ using long division.
$\begin{matrix}
& 3x^2 & -3x &+1 & & \leftarrow &Quotient\\
&-- &-- &--&--& \\
3x+2) &9x^3&-3x^2&-3x&+4 & \\
& 9x^3 & +6x^2 & & & \leftarrow &3x^2(3x+2) \\
& -- & -- & & & \leftarrow &subtract \\
& 0 & -9x^2 & -3x & & \\
& & -9x^2 & -6x & & \leftarrow & -3x(3x+2) \\
& & -- & -- & & \leftarrow & subtract \\
& & 0&3x &+4 & \\
& & & 3x& +2 & \leftarrow & 1(3x+2) \\
& & & -- & -- & \leftarrow & subtract \\
& & & 0 & +2 & \leftarrow & Remainder
\end{matrix}$
The answer is
$\Rightarrow Quotient + \frac{Remainder}{Divisor}$
$\Rightarrow 3x^2 -3x+1+\frac{2}{3x+2}$.
