Answer
$Q(x)=6x^{3}+6x^{2}+x+\displaystyle \frac{1}{3},\quad R(x)= \frac{7}{9}$
Work Step by Step
$\left.\begin{array}{l}
- \frac{2}{3} \ \lfloor \\ \\ \\\\ \end{array}\right.\begin{array}{rrrrr}
6 & 10 & 5 & 1 & 1 \\\hline
& -4 & -4 & -\displaystyle \frac{2}{3} & - \displaystyle \frac{2}{9} \\\hline
6 & 6 & 1 & \displaystyle \frac{1}{3} &|\displaystyle \ \ \ \frac{7}{9} \end{array}$
$Q(x)=6x^{3}+6x^{2}+x+\displaystyle \frac{1}{3},\quad R(x)= \frac{7}{9}$
