Chapter 8.5, Problem 3BGP

To determine

To factor: The polynomial $3np+15p-4n-20$

Answer to Problem 3BGP

  $\left(n+5\right)\left(3p-4\right)$

Explanation of Solution

Given:

  $3np+15p-4n-20$

Calculation:

The given polynomial is $3np+15p-4n-20$

Make groups as shown below

  $\left(3np+15p\right)+\left(-4n-20\right)$

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

  $\begin{array}{l}\left(3np+15p\right)+\left(-4n-20\right)\\ =3p\left(n+5\right)-4\left(n+5\right)\\ =\left(n+5\right)\left(3p-4\right)\end{array}$

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