Chapter 6 - Section 6.4 - Dividing Polynomials: Long Division and Synthetic Division - Exercise Set - Page 370: 19

$2x^3+\dfrac{9}{2}x^2+10x+21+\dfrac{42}{x-2}$

Using the long division method below, then \begin{array}{l}\require{cancel}\left( 2x^4+\dfrac{1}{2}x^3+x^2+x \right)\div( x-2 )\\= 2x^3+\dfrac{9}{2}x^2+10x+21+\dfrac{42}{x-2} .\end{array}