Answer
$\displaystyle \frac{7}{3}$
Work Step by Step
Remainder Theorem:
If the polynomial $P(x)$ is divided by $x-c$ , then the remainder is the value $P(c)$ .
$\left.\begin{array}{l}
2/3 \ \lfloor \\ \\ \\ \\ \end{array}\right.\begin{array}{rrrrr}
3 & 4 & -2 & 1 \\\hline
& 2 & 4 & \displaystyle \frac{4}{3} \\\hline
3 & 6 & 2 &|\displaystyle \ \ \ \frac{7}{3} \end{array}$
$R(x)=P(\displaystyle \frac{2}{3})=\frac{7}{3}$
