Chapter 8.3, Problem 11OE

To determine

To find : the quotient and remainder of division

Answer to Problem 11OE

The quotient is $x$ and remainder is $6$

Explanation of Solution

Given information : $\frac{x^2+5x+6}{x+5}$

Calculation :

  $\frac{x^2+5x+6}{x+5}$

Separate into two fractions

Write as quotient $+\frac{remainder}{x}$

  $\begin{array}{l}\frac{x\left(x+5\right)+6}{x+5}\\ \frac{x\left(x+5\right)}{\left(x+5\right)}+\frac{6}{\left(x+5\right)}\\ x+\frac{6}{\left(x+5\right)}\end{array}$

So, the quotient is $x$ and the remainder is $6$