Algebra (Period 5)

Using the Distributive Property 8-5

Using the Distributive Property to factor the GCF

(Your book also introduces “factoring by grouping” in this section but we will come back to that in a few days… We will also skip the ZERO PRODUCTS PROPERTY—for now)

Factoring is a skill that you MUST understand to be successful in high level math
Factoring is simply undoing multiplying.
Factoring uses the concept of DIVIDING
You are actually undoing the Distributive Property
How? You look for the most of every common factorà the GCF
Then you pull out the GCD (divide it out) from each term placing the GCF in front of a set of {{HUGS}}  parentheses

EXAMPLE:
Factor :  4m²n³ + 2m²n² + 6m²n
Step 1: What does each term have in common? (What is the GCF?)
They each can be divided by  2m²n  . Right ?
Step 2: Put the GCF in front of a set of {{HUGS}} and divide each term by the GCF

Step 3: Simplify and you get
2m²n(2n²+ n + 3)
Step 4: Check your answers!! Always check your factoring of the GCF by distributing back. (It should be the same thing!)

Another just as important check:
Make sure you have factored out the entire GCFà Look inside the parentheses and ask yourself:
Is there any common factors remaining between the terms?
If there is, you haven’t factored out the GREATEST Common Factor.

For example: Let’s say in the prior example that you only factored out 2mn

You would have:

 

Which would be    2mn( 2mn +mn +3m)
If you just check by distributing back, the problem will check…

BUT

Look inside the (  ) and notice that each term still has a common factor of m. So this would not be the fully factored form. Make sure you always look inside your {{HUGS}}

Relatively Prime Terms- terms with no common factors. That means that they cannot be factored ( GCF = 1)
We say they are “NOT Factorable” or “PRIME”