Chapter 11.5, Problem 20PPS

To determine

To calculate: To find the quotient

Answer to Problem 20PPS

The quotient is $\left(r-11\right)$

Explanation of Solution

Given information: Expression is $\left(r^2-12r+11\right)÷\left(r-1\right)$

Calculation:

Expression is given as

  $\left(r^2-12r+11\right)÷\left(r-1\right)$

On solving the above expression:

  $\begin{array}{l}\Rightarrow \frac{r^2-12r+11}{r-1}\\ \Rightarrow \frac{r^2-11r-r+11}{r-1}\\ \Rightarrow \frac{r\left(r-11\right)-1\left(r-11\right)}{r-1}\\ \Rightarrow \frac{\left(r-11\right)\left(r-1\right)}{r-1}\\ \Rightarrow \frac{\left(r-11\right)}{1}\\ \Rightarrow \left(r-11\right)\end{array}$

Conclusion:

Hence, the quotient is $\left(r-11\right)$