Chapter 8.6, Problem 1AGP

To determine

To factor: The polynomial $d^2+11d+24$

Answer to Problem 1AGP

  $\left(d+8\right)\left(d+3\right)$

Explanation of Solution

Given:

  $d^2+11d+24$

Calculation:

The given polynomial is $d^2+11d+24$

Rewrite the middle term as $11d=8d+3d$ . So, the polynomial becomes

  $d^2+8d+3d+24$

Make group as shown below

  $\left(d^2+8d\right)+\left(3d+24\right)$

Factor out the GCF from each of the group

  $d\left(d+8\right)+3\left(d+8\right)$

Finally, factored out the common factor

  $\left(d+8\right)\left(d+3\right)$

Therefore, the factored form of the given polynomial is $\left(d+8\right)\left(d+3\right)$