Chapter 8.6, Problem 13PPS

To determine

To factor: The polynomial $a^2+8a-48$ . Confirm your answer using a graphing calculator.

Answer to Problem 13PPS

  $\left(a+12\right)\left(a-4\right)$

Explanation of Solution

Given:

  $a^2+8a-48$

Calculation:

The given polynomial is $a^2+8a-48$

Rewrite the middle term as $8a=12a-4a$ . So, the polynomial becomes

  $a^2+12a-4a-48$

Make group as shown below

  $\left(a^2+12a\right)+\left(-4a-48\right)$

Factor out the GCF from each of the group

  $a\left(a+12\right)-4\left(a+12\right)$

Finally, factored out the common factor

  $\left(a+12\right)\left(a-4\right)$

Therefore, the factored form of the given polynomial is $\left(a+12\right)\left(a-4\right)$

Now, using a graphing calculator, the factor of the polynomial is given by

  $\left(a+12\right)\left(a-4\right)$

So, the answer is verified.