Chapter 8.5, Problem 31PPS

To determine

To factor: The polynomial $5br-25b+2r-10$

Answer to Problem 31PPS

  $\left(r-5\right)\left(5b+2\right)$

Explanation of Solution

Given:

  $5br-25b+2r-10$

Calculation:

The given polynomial is $5br-25b+2r-10$

Make groups as shown below

  $\left(5br-25b\right)+\left(2r-10\right)$

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

  $\begin{array}{l}\left(5br-25b\right)+\left(2r-10\right)\\ =5b\left(r-5\right)+2\left(r-5\right)\\ =\left(r-5\right)\left(5b+2\right)\end{array}$

So, the factored form is $\left(r-5\right)\left(5b+2\right)$