Chapter 3, Polynomial and Rational Functions - Section 3.3 - Dividing Polynomials - 3.3 Exercises - Page 310: 12

$4x^{3}+7x+9=(2x+1)(2x^{2}-x+4)+5$

$\left[\begin{array}{l} \\ 2x+1\ )\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \end{array}\right. \left.\begin{array}{rrrrrr} 2x^{2} & -x & +4 & & \\ \hline 4x^{3} & & +7x & +9 & \\ 4x^{3} & +2x^{2} & & & \\ -- & -- & & & \\ & -2x^{2} & +7x & +9 & \\ & -2x^{2} & -x & & \\ & -- & -- & & \\ & & 8x & +9 & \\ & & 8x & +4 & \\ & & -- & -- & \\ & & & 5 & \end{array}\right]$ $Q(x)=2x^{2}-x+4,\quad R(x)=5$ In the form $P(x)=D(x)\cdot Q(x)+R(x),$ $4x^{3}+7x+9=(2x+1)(2x^{2}-x+4)+5$