Chapter 8.5, Problem 39PPS

To determine

To factor: The polynomial $20p^2+15p+8pr+6r$

Answer to Problem 39PPS

  $\left(4p+3\right)\left(5p+2r\right)$

Explanation of Solution

Given:

  $20p^2+15p+8pr+6r$

Calculation:

The given polynomial is $20p^2+15p+8pr+6r$

Make groups as shown below

  $\left(20p^2+15p\right)+\left(8pr+6r\right)$

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

  $\begin{array}{l}\left(20p^2+15p\right)+\left(8pr+6r\right)\\ =5p\left(4p+3\right)+2r\left(4p+3\right)\\ =\left(4p+3\right)\left(5p+2r\right)\end{array}$

So, the factored form is $\left(4p+3\right)\left(5p+2r\right)$