Chapter 3, Polynomial and Rational Functions - Section 3.3 - Dividing Polynomials - 3.3 Exercises - Page 310: 18

$Q(x)=\displaystyle \frac{1}{3}x^{2}+\frac{1}{3}x+\frac{2}{3},\quad R(x)=-1$

$ \left.\begin{array}{l} \\ 3x+6\ )\\ \\ \\ \\ \\ \\ \\\\\\ \\ \end{array}\right. \begin{array}{rrrrrr} \frac{1}{3}x^{2} & +\frac{1}{3}x & +\frac{2}{3} & & \\ \hline x^{3} & +3x^{2} & +4x & +3 & \\ x^{3} & +2x^{2} & & & \\ -- & -- & & & \\ & x^{2} & +4x & +3 & \\ & x^{2} & +2x & & \\ & -- & -- & & \\ & & 2x & +3 & \\ & & 2x & +4 & \\ & & -- & -- & \\ & & & -1 & \end{array} $ $Q(x)=\displaystyle \frac{1}{3}x^{2}+\frac{1}{3}x+\frac{2}{3},\quad R(x)=-1$