Chapter 8.6, Problem 55PFA

To determine

To find: which expression is a factor of the polynomial $x^2-3x-108$

Answer to Problem 55PFA

  $\left(x-12\right)$ is a factor of the given expression.

B is the correct option

Explanation of Solution

Given:

Options are:

  $\begin{array}{l}\mathrm{A }\left(x-9\right)\\ \mathrm{B }\left(x-12\right)\\ \mathrm{C }\left(x+4\right)\\ \mathrm{D }\left(x-27\right)\end{array}$

Calculation:

The given expression is $x^2-3x-108$

Now, write the middle term $3x$ as $-12x+9x$

  $x^2-12x+9x-108$

Make groups as shown below

  $\left(x^2-12x\right)+\left(9x-108\right)$

Factored out the GCF from each group

  $x\left(x-12\right)+9\left(x-12\right)$

Factored out the common term

  $\left(x-12\right)\left(x+9\right)$

Thus, $\left(x-12\right)$ is a factor of the given expression.

B is the correct option.