1. Magicians

3. Factoring Expressions Greatest Common Factor (GCF)
Difference of 2 Squares 3

4. I can factor expressions using the Greatest Common Factor Method (GCF)
Objectives
I can factor expressions using the Greatest Common Factor Method (GCF)
I can factor expressions using the Difference of 2 Squares Method 4

5. What is Factoring?
Quick Write: Write down everything you know about Factoring from Algebra-1 and Geometry?
You can use Bullets or give examples
2 Minutes
Share with partner! 5

6. Factoring?
Factoring is a method to find the basic numbers and variables that made up a product.
(Factor) x (Factor) = Product
Some numbers are Prime, meaning they are only divisible by themselves and 1 6

7. Method 1
Greatest Common Factor (GCF) – the greatest factor shared by two or more numbers, monomials, or polynomials
ALWAYS try this factoring method 1st before any other method
Divide Out the Biggest common number/variable from each of the terms

8. Greatest Common Factors aka GCF’s
Find the GCF for each set of following numbers.
Find means tell what the terms have in common.
Hint: list the factors and find the greatest match.
2, 6
-25, -40
6, 18
16, 32
3, 8 2 -5 6 16 1
No common factors? GCF =1

9. Greatest Common Factors aka GCF’s
Find the GCF for each set of following numbers.
Hint: list the factors and find the greatest match.
x, x2
x2, x3
xy, x2y
2x3, 8x2
3x3, 6x2
4x2, 5y3 x x2 xy
2x2
3x2 1
No common factors? GCF =1

10. Greatest Common Factors aka GCF’s
Factor out the GCF for each polynomial: Factor out means you need the GCF times the remaining parts.
a) 2x + 4y
5a – 5b
18x – 6y
2m + 6mn
5x2y – 10xy
2(x + 2y)
How can you check?
5(a – b)
6(3x – y)
2m(1 + 3n)
5xy(x - 2)

11. FACTORING by GCF Take out the GCF EX: 15xy2 – 10x3y + 25xy3 How:
Find what is in common in each term and put in front. See what is left over.
Check answer by distributing out.
Solution:
5xy( )
3y – 2x2 + 5y2

12. FACTORING Take out the GCF EX: 2x4 – 8x3 + 4x2 – 6x How:
Find what is in common in each term and put in front. See what is left over.
Check answer by distributing out.
Solution: 2x
(x3 – 4x2 + 2x – 3)

13. Ex 1
15x2 – 5x
GCF = 5x
5x(3x - 1) 13

14. Ex 2
8x2 – x
GCF = x
x(8x - 1) 14

15. Ex 3
8x2y4+ 2x3y5 - 12x4y3
GCX = 2x2y3
2x2y3 (4y + xy2 – 6x2) 15

16. Difference of Two Squares a2 – b2 = (a + b)(a - b)
Method #2
Difference of Two Squares
a2 – b2 = (a + b)(a - b) 16

17. What is a Perfect Square
Any term you can take the square root evenly (No decimal) 25 36 1 x2 y4 17

18. Difference of Perfect Squares
x2 – 4 =
the answer will look like this: ( )( )
take the square root of each part:
( x 2)(x 2)
Make 1 a plus and 1 a minus:
(x + 2)(x - 2 )

19. FACTORING Difference of Perfect Squares EX: x2 – 64 How:
Take the square root of each part. One gets a + and one gets a -.
Check answer by FOIL.
Solution:
(x – 8)(x + 8)

20. YOUR TURN!!

21. Example 1
(9x2 – 16)
(3x + 4)(3x – 4) 21

22. Example 2
x2 – 16
(x + 4)(x –4) 22

23. Ex 3
36x2 – 25
(6x + 5)(6x – 5) 23

24. ALWAYS use GCF first More than ONE Method
It is very possible to use more than one factoring method in a problem
Remember:
ALWAYS use GCF first 24

25. 2nd term is the diff of 2 squares 2x(b + 5)(b - 5)
Example 1
2b2x – 50x
GCF = 2x
2x(b2 – 25)
2nd term is the diff of 2 squares
2x(b + 5)(b - 5) 25

26. Example 2 32x3 – 2x GCF = 2x 2x(16x2 – 1)
2nd term is the diff of 2 squares
2x(4x + 1)(4x - 1) 26

27. Exit Slip
On the back of your Yellow Sheet write these 2 things:
1. Define what factors are?
2. What did you learn today t?
Put them in Basket on way out!

28. Homework
WS 5-1 28