Answer
$3x^{2}+3x-3$
Work Step by Step
Dividing with $x-c\displaystyle \qquad...\qquad c=-\frac{1}{3}.$
Don't forget to place 0's for the missing terms.
$\begin{array}{rrrrrrrr}
\underline{\frac{1}{3}}| &3 & 2 & -4 & 1 & & \\
& & 1 & 1 &-1 & & \\
& --& -- &-- &-- & & \\
&3 & 3 & -3 & 0 & & \end{array}$
Quotient = $3x^{2}+3x-3$
Remainder = $0$
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{3x^{3}+2x^{2}-4x+1}{x-\frac{1}{3}}$ = $3x^{2}+3x-3$
