Chapter 8.5, Problem 22PPS

To determine

To factor: The polynomial $a^2-4a-24+6a$

Answer to Problem 22PPS

  $\left(a-4\right)\left(a+6\right)$

Explanation of Solution

Given:

  $a^2-4a-24+6a$

Calculation:

The given polynomial is $a^2-4a-24+6a$

Make groups as shown below

  $\left(a^2-4a\right)+\left(-24+6a\right)$

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

  $\begin{array}{l}\left(a^2-4a\right)+\left(-24+6a\right)\\ =a\left(a-4\right)+6\left(a-4\right)\\ =\left(a-4\right)\left(a+6\right)\end{array}$

So, the factored form is $\left(a-4\right)\left(a+6\right)$