2. Magicians

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

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

6. 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!

7. 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

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

9. 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. a)2, 6 b)-25, -40 c)6, 18 d)16, 32 e)3, 8 2 -5 6 16 1 No common factors? GCF =1

10. Find the GCF for each set of following numbers. Hint: list the factors and find the greatest match. a)x, x 2 b)x 2, x 3 c)xy, x 2 y d)2x 3, 8x 2 e)3x 3, 6x 2 f)4x 2, 5y 3 x x2x2 xy 2x 2 Greatest Common Factors aka GCF’s 3x 2 1 No common factors? GCF =1

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

12. FACTORING by GCF Take out the GCFEX: 15xy 2 – 10x 3 y + 25xy 3 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 – 2x 2 + 5y 2

13. FACTORING Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 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 (x 3 – 4x 2 + 2x – 3)

14. Ex 1 15x 2 – 5x GCF = 5x 5x(3x - 1)

15. Ex 2 8x 2 – x GCF = x x(8x - 1)

16. Ex 3 8x 2 y 4 + 2x 3 y 5 - 12x 4 y 3 GCX = 2x 2 y 3 2x 2 y 3 (4y + xy 2 – 6x 2 )

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

18. What is a Perfect Square Any term you can take the square root evenly (No decimal) 25 36 1 x 2 y 4

19. Difference of Perfect Squares x 2 – 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 )

20. FACTORING Difference of Perfect Squares EX: x 2 – 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)

21. YOUR TURN!!

22. Example 1 (9x 2 – 16) (3x + 4)(3x – 4)

23. Example 2 x 2 – 16 (x + 4)(x –4)

24. Ex 3 36x 2 – 25 (6x + 5)(6x – 5)

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

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

27. Example 2 32x 3 – 2x GCF = 2x 2x(16x 2 – 1) 2 nd term is the diff of 2 squares 2x(4x + 1)(4x - 1)

28. Exit Slip On the back of your Yellow Sheet write these 2 things: 1. Define what factors are? 2. What did you learn today that was not on the front of your yellow sheet? Put them in Basket on way out!

29. Homework WS 5-1