Math 7 ( Period 4)

GREATEST COMMON  FACTOR 
Factoring OUT the GCF

( the Distributive Property backwards—revisited. At the beginning of the year we reviewed the DP and talked about using it BACKWARDS to look at whether it was easier to simply use O3 to simplify—rathr than distribute. Today I will revisit this concept but we will call it FACTORING the GCF Factor the GCF means

1) find the GCF of 2 or more terms

2) set up a pair of (  )

3) Place the GCF in front of the ( )

4) divide the GCF OUT OF EACH term and place the quotients inside the (  ) with the applicable sign ( + or - )

Factor 36 + 45

the gcf is 9

9(4 + 5)

Notice when you look side the (    ) there shouldn’t be an common factors of the 2 terms—OR you did not USE the GCF.

Notice: You will get the same results either way because FACOTRING THE GCF DOESN’T change the value EVER!!!

36 + 45 = 81

9(4 + 5) = 9(4) + 9(5) = 81

The reason we need to know this is because of variables – so let’s look at a couple of algebraic terms

Factor 36a²b²c² – 45a²c⁵d

The GCF is 9a²c²

 9a²c² (4b²-5c³d)

If you now distribute back, you will get exactly what you started with.

If you look inside the (  )’s you will see that there are no longer any common factors between the 2 terms—they are now relatively prime. This example shows that you get c³ because you factored out 2 of the c’s leaving 3 more of them 
inside the (  )’s.