Chapter 8.5, Problem 21PPS

To determine

To factor: The polynomial $fg-5g+4f-20$

Answer to Problem 21PPS

  $\left(f-5\right)\left(g+4\right)$

Explanation of Solution

Given:

  $fg-5g+4f-20$

Calculation:

The given polynomial is $fg-5g+4f-20$

Make groups as shown below

  $\left(fg-5g\right)+\left(4f-20\right)$

So, factored out the GCF from each of the group and then factored out the common factor

  $\begin{array}{l}\left(fg-5g\right)+\left(4f-20\right)\\ =g\left(f-5\right)+4\left(f-5\right)\\ =\left(f-5\right)\left(g+4\right)\end{array}$

So, the factored form is $\left(f-5\right)\left(g+4\right)$