1. Factoring Polynomials
Ann Georgy and Tiffany Kwok
Period 6

2. Doris list on how to factor
Polynomial
LOOK FOR A GCF or GMF!
Factor as productof Binomials
Not Factorable
Special Product
Factor of Grouping
Difference of Squares
PST
3. How to find GMF
Example:53and 102

So the GMF is
You can figure out the GMF by writing it out, using Prime Factorization
=5

=25

G=52

4. Factoring Polynomials
Like always find the GMF first. In this case the GMF is 43

Next, divide each term by the GMF. SO that way each term will be the product of the GCF.
Example:84123

GMF: 43

844312343

=43(23)

The 84became 2and 123became 3 afterbeing divided by 43

5. What do these to group have in common?
Use FOIL to double check your work
Before you do anything, group monomials that have a GCF.
Look they both have(31)so now all you have to do is factor it out!

Factor by Grouping
Example: 15415+12312

(15415)+(12312)

15(31)+12(31)

(31)(15+12)

3115+12=15415+12312

6. What if they are opposites?
Example: 5210+632

Like before, group the terms the monomials that have something in common.
Find the GMF of each group!
Oh my! Look (x-2) and (2-x) are two different things. So they dont have a common factor?
NO! Actually they do, multiply (2-x) by -1 to change it around!
Now factor it out, and use FOIL to double check your work!
(-2+x) is the same as (x-2).
(5210)+(632)

5(2)+3(2)

5(2)+3(1)(2)
5232+
523(2)
(2)(53)

(2)(53)= 5210+632

7. Factoring Binomails: 2++

You must find a pair of number, when added equals to B and gives a product of C.
(,)

=





t+w=b

8. Product of Binomials: 2++

What are some factors of 20 that add up to 9?
Look, the group (4,5) add up to 9 and have a product of 20.
The first term is 2, so thats why the variables need to have a coefficient of 1. Or (+)(+)

Use FOIL to double check you work!
Example:2+9+20
20=1,20,2,10,4,5

(+4)(+5)

(+4)(+5)=2+9+20

9. What if is negative?

It looks like the pair (2,-16) satisfies both these requirements!
Well, this is almost the same, what pair of numbers gives a product a-32, and a sum of -14?
Like before because 2 is the first term, the variable terms need to have a coefficient of 1.

Use FOIL to double check you work!
Example:214x32

32=1,32,2,16,4,8,32,1,(2,16)

(+2)(16)

(+2)(16)= 214x32

10. Product of Binomials: 2++

Use the FOIL method, to double check if it works!
Hey lets try the pair (2,5), and see if it works.Remember to use the form (x+) (x+)!

Look here a=3, b=12 and c=10.Try to find a pair of numbers in which there sum is 12 and product is 10.Well this is just guess and check!
Split up32 !

Example: 32+12x+10

10=1,10,(2,5)

(2+2)(+5)

2+2+5=
32+12x+10

11. Perfect Square Trinomial
In this case the pair is (-14,-14). Lets try it out.
Use FOIL to see if it works.
Yes thats right, it is equal to(14)2!

A Perfect Square Trinomial is when you square a binomial quantity.
Example: 228+196

Like before find a pair of numbers that has a sum of -28 and a product of 196
IT WORKS! But do you notice that (x-14) and (x-14) is the same? So that means it is equivalent to
(14)(14)

(14)(14)=21414+196

(14)2

12. Difference of Squares
The -562 cancels out 562 leaving us with 644492

Factor out the two monomials!
Use FOIL to double check your work!
A difference of Square's is when a square number is subtracted from another square number.
Example: 644492

(82+7y)(827y)

(82+7y)827y=644562+562492

(82+7y)(827y)