Question

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

Answer 1

`(9f-7)(g-5)`

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 `-45f` and `-5xx9=45` so try:

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

We need `-7g` so try `(9f-7)`

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