Factoring GCF difference of squares.ppt
- 1. Magicians They are all MASTERS of Magic!!
- 2. It is my GOAL for each of you to become MASTERS of FACTORING
- 3. Factoring Expressions - Greatest Common Factor (GCF) - Difference of 2 Squares
- 4. Objectives • I can factor expressions using the Greatest Common Factor Method (GCF) • I can factor expressions using the Difference of 2 Squares Method
- 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!
- 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
- 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. 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
- 9. Find the GCF for each set of following numbers. Hint: list the factors and find the greatest match. a) x, x2 b) x2, x3 c) xy, x2y d) 2x3, 8x2 e) 3x3, 6x2 f) 4x2, 5y3 x x2 xy 2x2 Greatest Common Factors aka GCF’s 3x2 1 No common factors? GCF =1
- 10. 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) 5x2y – 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?
- 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)
- 14. Ex 2 •8x2 – x •GCF = x •x(8x - 1)
- 15. Method #2 •Difference of Two Squares •a2 – b2 = (a + b)(a - b)
- 16. What is a Perfect Square • Any term you can take the square root evenly (No decimal) • 25 • 36 • 1 • x2 • y4 5 6 1 x 2 y
- 17. 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 )
- 18. 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)
- 19. YOUR TURN!! Using White Boards
- 20. Example 1 •(9x2 – 16) •(3x + 4)(3x – 4)
- 21. Example 2 •x2 – 16 •(x + 4)(x –4)
- 22. Ex 3 •36x2 – 25 •(6x + 5)(6x – 5)
- 23. More than ONE Method • It is very possible to use more than one factoring method in a problem • Remember: • ALWAYS use GCF first
- 24. Example 1 • 2b2x – 50x • GCF = 2x • 2x(b2 – 25) • 2nd term is the diff of 2 squares • 2x(b + 5)(b - 5)
- 25. Example 2 • 32x3 – 2x • GCF = 2x • 2x(16x2 – 1) • 2nd term is the diff of 2 squares • 2x(4x + 1)(4x - 1)
- 26. Exit Slip • On a post it note write these 2 things: (with your name) • 1. Define what factors are? • 2. What did you learn today about factoring? • Put them on the bookshelf on the way out!