Chapter 8.5, Problem 30PPS

To determine

To factor: The polynomial $vp+12v+8p+96$

Answer to Problem 30PPS

  $\left(p+12\right)\left(v+8\right)$

Explanation of Solution

Given:

  $vp+12v+8p+96$

Calculation:

The given polynomial is $vp+12v+8p+96$

Make groups as shown below

  $\left(vp+12v\right)+\left(8p+96\right)$

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

  $\begin{array}{l}\left(vp+12v\right)+\left(8p+96\right)\\ =v\left(p+12\right)+8\left(p+12\right)\\ =\left(p+12\right)\left(v+8\right)\end{array}$

So, the factored form is $\left(p+12\right)\left(v+8\right)$