Chapter 3, Polynomial and Rational Functions - Section 3.3 - Dividing Polynomials - 3.3 Exercises - Page 310: 13

$8x^{4}+4x^{3}+6x^{2}=(2x^{2}+1)(4x^{2}+2x+1)+(-2x-1)$

$\left.\begin{array}{l} \\\\ 2x^{2}+1\ )\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \end{array}\right. \left.\begin{array}{lllll} 4x^{2} & +2x & +1 & & \\ \hline 8x^{4} & +4x^{3} & +6x^{2} & & \\ 8x^{4} & & +4x^{2} & & \\ -- & -- & -- & & \\ & 4x^{3} & +2x^{2} & & \\ & 4x^{3} & & +2x & \\ & -- & -- & -- & \\ & & 2x^{2} & -2x & \\ & & 2x^{2} & & +1\\ & & -- & -- & --\\ & & & -2x & -1 \end{array}\right.$ $Q(x)=4x^{2}+2x+1,\quad R(x)=-2x-1$ In the form $P(x)=D(x)\cdot Q(x)+R(x),$ $8x^{4}+4x^{3}+6x^{2}=(2x^{2}+1)(4x^{2}+2x+1)+(-2x-1)$