Algebra Period 4

Factoring Polynomials 6-1

Chapter 5 was a very important chapter that you cannot survive without...

CHAPTER 6 IS EVEN MORE IMPORTANT FOR HIGH SCHOOL!!!



As I stated-- these chapters are the Meat & Potatoes of Algebra!!

REMEMBER:

FACTORING WILL NEVER CHANGE THE ORIGINAL VALUE OF THE POLYNOMIAL SO YOU SHOULD ALWAYS CHECK BY MULTIPLYING BACK!!!!
(You'll either distribute or FOIL...that's what you learned how to do in Chapter 5!)


CHAPTER 6-1: FACTORING THE GCF

Factoring is a skill that you must understand to be successful in higher level math!!!

We did a simple version of this back in Chapter 1!


Factoring is simply UNDOING multiplying

Say you multiplied 5 by 10 and got 50

How would you undo it?
DIVIDE by 5!

So FACTORING uses the concept of DIVIDING.

You're actually undoing the DISTRIBUTIVE PROPERTY.

How?

You look for the most of every common factor....the GCF!

Then you pull out the GCF (divide it out of) from each term, 
Placing the GCF in front of ( )


EXAMPLE:

FIRST,
DISTRIBUTE:

2m²n(2n² + n + 3)


4m² n³ + 2m² n² + 6m² n



Now, pretend you don't want the 2m²n distributed anymore...
What should you end up with once you UNDO the Distributive Property?

2m² n (2n² + n + 3)



That's exactly what you started with!

So is it that easy?

Well yes... and no...

Yes because that is the answer
 and

No because it was only that easy because I gave you how it started!

You won't know how it started in a real problem!
THIS IS AN EXAMPLE THE WAY YOU WOULD USUALLY SEE IT.

The question would say:
FACTOR: 
4m² n³ + 2m² n² + 6m² n



Step 1: What does each term have in common (what is the GCF) ?

They each can be divided by 2m² n


Step 2: Put the GCF in front of a set of (   ) and divide each term by the GCF
2m² n [ (4m² n³)/2m² n + (2m² n²)/2m² n + (6m²n/2m² n]

Step 3: SIMPLIFY and you'll get:

2m²n (2n² + n + 3)



Step 4: Check your answer!!!!!

Always check your factoring of the GCF by distributing back!

(incognito, it should be the same thing)



RELATIVELY PRIME TERMS ARE 
TERMS WITH NO COMMON FACTORS
 THAT MEANS THAT THEY CANNOT BE FACTORED (GCF = 1)
We say they are "not factorable"