Chapter 8.5, Problem 34PPS

To determine

To factor: The polynomial $rp-9r+9p-81$

Answer to Problem 34PPS

  $\left(p-9\right)\left(r+9\right)$

Explanation of Solution

Given:

  $rp-9r+9p-81$

Calculation:

The given polynomial is $rp-9r+9p-81$

Make groups as shown below

  $\left(rp-9r\right)+\left(9p-81\right)$

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

  $\begin{array}{l}\left(rp-9r\right)+\left(9p-81\right)\\ =r\left(p-9\right)+9\left(p-9\right)\\ =\left(p-9\right)\left(r+9\right)\end{array}$

So, the factored form is $\left(p-9\right)\left(r+9\right)$