# How do you factor 9fg-45f-7g+35?

May 4, 2017

$\left(9 f - 7\right) \left(g - 5\right)$

#### Explanation:

Note that both 7 and 5 are prime numbers and 5 is one of the factors of 35 and 45. Also 5 is not a factor of 9. So I choose to test the start point of:

(9f+-?)(g+-)" "=" "9fg.....

But ?xx?=+35" "=>5xx7
As the 35 is positive both signs are the same.
We need $- 45 f$ and $- 5 \times 9 = 45$ so try:

(9f+-?)(g-5)" "=" "9fg -45f.....

We need $- 7 g$ so try $\left(9 f - 7\right)$

(9f-7)(g-5)" "=" "9fg -45f-7g+35 color(red)(larr" Works!")