Chapter 8.3, Problem 12WE

To determine

To divide : the expression

Answer to Problem 12WE

The quotient is $3x-1$ and remainder is $5x-2$

Explanation of Solution

Given information : The expression is $\frac{6x^3-5x^2+15x-5}{2x^2-x+3}$

Calculation :

By long division method

  $\begin{array}{l}2x^2-x+3\begin{array}{c}\hfill 3x-1\\ \hfill \overline{)\begin{array}{l}6x^3-5x^2+15x-5\\ 6x^3-3x^2+9x\end{array}}\end{array}\\ \underset{\_}{-+-}\\ -2x^2+6x-5\\ -2x^2+x-3\\ \underset{\_}{+-\text{ + }}\\ 5x-2\\ 3x-1+\frac{5x-2}{2x^2-x+3}\end{array}$