Chapter 11, Problem 34SGR

To determine

To find: the given quotient.

Answer to Problem 34SGR

The quotient is $x^2+x-19-\frac{36}{x-3}$

Explanation of Solution

Given:

  $\left(x^3-2x^2-22x+21\right)÷\left(x-3\right)$

Calculation:

The quotient of the expression is calculated using long division method below.

  $x-3\begin{array}{c}\hfill x^2+x-19\\ \hfill \overline{)\begin{array}{l}{x}^3-2x^2-22x+21\\ \underset{\_}{x^3-3x^2}\\ x^2-22x\\ \underset{\_}{x^2-3x}\\ -19x+21\\ \underset{\_}{-19x+57}\\ -36\end{array}}\end{array}$

Conclusion:

The quotient is $x^2+x-19-\frac{36}{x-3}$