Chapter 8.3, Problem 10WE

To determine

To divide : the expression

Answer to Problem 10WE

The quotient is $3y^2+2y-3$ and remainder is $-9$

Explanation of Solution

Given information : The expression is $\frac{15y^3+y^2-21y}{5y-3}$

Calculation :

By long division method

  $\begin{array}{l}5y-3\begin{array}{c}\hfill 3y^2+2y-3\\ \hfill \overline{)\begin{array}{l}15y^3+y^2-21y\\ 15y^3-9y^2\end{array}}\end{array}\\ \underset{\_}{-+}\\ 10y^2-21y\\ 10y^2-6y\\ \underset{\_}{-\text{ + }}\\ -15y\\ \underset{\_}{\begin{array}{l}-15y+9\\ +-\end{array}}\\ -9\\ 3y^2+2y-3-\frac{9}{5y-3}\end{array}$