Chapter 8.5, Problem 8CYU

To determine

To factor: The polynomial $9fg-45f-7g+35$

Answer to Problem 8CYU

  $\left(g-5\right)\left(9f-7\right)$

Explanation of Solution

Given:

  $9fg-45f-7g+35$

Calculation:

The given polynomial is $9fg-45f-7g+35$

Make groups as shown below

  $\left(9fg-45f\right)+\left(-7g+35\right)$

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

  $\begin{array}{l}\left(9fg-45f\right)+\left(-7g+35\right)\\ =9f\left(g-5\right)-7\left(g-5\right)\\ =\left(g-5\right)\left(9f-7\right)\end{array}$

So, the factored form is $\left(g-5\right)\left(9f-7\right)$