Chapter 8.6, Problem 3BGP

To determine

To factor: The polynomial $r^2-2r-24$

Answer to Problem 3BGP

  $\left(r-6\right)\left(r+4\right)$

Explanation of Solution

Given:

  $r^2-2r-24$

Calculation:

The given polynomial is $r^2-2r-24$

Rewrite the middle term as $-2r=-6r+4r$ . So, the polynomial becomes

  $r^2-6r+4r-24$

Make group as shown below

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

Factor out the GCF from each of the group

  $r\left(r-6\right)+4\left(r-6\right)$

Finally, factored out the common factor

  $\left(r-6\right)\left(r+4\right)$

Therefore, the factored form of the given polynomial is $\left(r-6\right)\left(r+4\right)$