Chapter 8.5, Problem 3AGP

To determine

To factor: The polynomial $rn+5n-r-5$

Answer to Problem 3AGP

  $\left(r+5\right)\left(n-1\right)$

Explanation of Solution

Given:

  $rn+5n-r-5$

Calculation:

The given polynomial is $rn+5n-r-5$

Make groups as shown below

  $\left(rn+5\right)+\left(-r-5\right)$

So, factored out the GCF from each of the group and then factored out the common factor

  $\begin{array}{l}\left(rn+5n\right)+\left(-r-5\right)\\ =n\left(r+5\right)-1\left(r+5\right)\\ =\left(r+5\right)\left(n-1\right)\end{array}$

So, the factored form is $\left(r+5\right)\left(n-1\right)$