Chapter 8.6, Problem 3AGP

To determine

To factor: The polynomial $y^2+13y-48$

Answer to Problem 3AGP

  $\left(y+16\right)\left(y-3\right)$

Explanation of Solution

Given:

  $y^2+13y-48$

Calculation:

The given polynomial is $y^2+13y-48$

Rewrite the middle term as $13y=16y-3y$ . So, the polynomial becomes

  $y^2+16y-3y-48$

Make group as shown below

  $\left(y^2+16y\right)+\left(-3y-48\right)$

Factor out the GCF from each of the group

  $y\left(y+16\right)-3\left(y+16\right)$

Finally, factored out the common factor

  $\left(y+16\right)\left(y-3\right)$

Therefore, the factored form of the given polynomial is $\left(y+16\right)\left(y-3\right)$