Chapter 8.6, Problem 31PPS

To determine

To factor: The polynomial $q^2+11qr+18r^2$

Answer to Problem 31PPS

  $\left(q+9r\right)\left(q+2r\right)$

Explanation of Solution

Given:

  $q^2+11qr+18r^2$

Calculation:

The given polynomial is $q^2+11qr+18r^2$

Rewrite the middle term as $11qr=9qr+2qr$ . So, the polynomial becomes

  $q^2+9qr+2qr+18r^2$

Make group as shown below

  $\left(q^2+9qr\right)+\left(2qr+18r^2\right)$

Factor out the GCF from each of the group

  $q\left(q+9r\right)+2r\left(q+9r\right)$

Finally, factored out the common factor

  $\left(q+9r\right)\left(q+2r\right)$

Therefore, the factored form of the given polynomial is $\left(q+9r\right)\left(q+2r\right)$