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Magicians

Learn the concepts of factoring in algebra and geometry, including GCF and Difference of 2 Squares methods. Practice problems and examples included.

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Magicians

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  1. Magicians

  2. Essential Question: • What is Factoring and How Can I use it? Adapted by Christopher Carnes, Rancho Viejo MS, Hemet, CA 2/3/2016

  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 Factorsaka 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. 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 Greatest Common Factorsaka GCF’s x x2 xy 2x2 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 5a – 5b 18x – 6y 2m + 6mn 5x2y – 10xy Greatest Common Factorsaka GCF’s 2(x + 2y) How can you check? 5(a – b) 6(3x – y) 2m(1 + 3n) 5xy(x - 2)

  11. FACTORING by GCF -2x2 5xy( ) 3y + 5y2

  12. FACTORING (x3 – 4x2 + 2x – 3) 2x

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

  14. Ex 2 • 8x2 – x • GCF = x • x(8x - 1)

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

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

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

  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 (x – 8)(x + 8)

  20. YOUR TURN!!

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

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

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

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

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

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

  27. Exit Slip • On your notes, write these 2 things: • 1. Define what factors are? • 2. What did you learn today about factoring?

  28. Homework • WB Page 125, 1-21 Odd

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