Chapter 8.5, Problem 5CYU

To determine

To factor: The polynomial $np+2n+8p+16$

Answer to Problem 5CYU

  $\left(p+2\right)\left(n+8\right)$

Explanation of Solution

Given:

  $np+2n+8p+16$

Calculation:

The given polynomial is $np+2n+8p+16$

Make groups as shown below

  $\left(np+2n\right)+\left(8p+16\right)$

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

  $\begin{array}{l}\left(np+2n\right)+\left(8p+16\right)\\ =n\left(p+2\right)+8\left(p+2\right)\\ =\left(p+2\right)\left(n+8\right)\end{array}$

So, the factored form is $\left(p+2\right)\left(n+8\right)$