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

1 Answer
Tony B
May 4, 2017

#(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!") #

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