Chapter 8.3, Problem 11WE

To determine

To divide : the expression

Answer to Problem 11WE

The quotient is $2t^2-t+3$ and remainder is $4$

Explanation of Solution

Given information : The expression is $\frac{6t^3+t^2+7y+10}{3t+2}$

Calculation :

By long division method

  $\begin{array}{l}3t+2\begin{array}{c}\hfill 2t^2-t+3\\ \hfill \overline{)\begin{array}{l}6t^3+t^2+7t+10\\ 6t^3+4t^2\end{array}}\end{array}\\ \underset{\_}{--}\\ -3t^2+7t\\ -3t^2-2t\\ \underset{\_}{+\text{ + }}\\ 9t+10\\ \underset{\_}{\begin{array}{l}9t+6\\ --\end{array}}\\ 4\\ 2t^2-t+3+\frac{4}{3t+2}\end{array}$