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Factoring GCF and Trinomials

Factoring GCF and Trinomials. Greatest Common Factor. The Greatest Common Factor is the largest number that will divide into a group of numbers. Examples: 6, 9 15, 55. GCF = 3. GCF = 5. 3. What is the greatest common factor??. 36. 24. The number 12. GCF with Variables.

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Factoring GCF and Trinomials

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  1. Factoring GCF and Trinomials

  2. Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers • Examples: • 6, 9 • 15, 55 GCF = 3 GCF = 5

  3. 3. What is the greatest common factor?? 36 24 The number 12

  4. GCF with Variables Note: With variables, the GCF will Always be the smallest exponent of a Common variable • Examples: • 12x3, 16x2 • 45a5, 50a7 GCF = 4x2 GCF = 5a5

  5. 6. What is the greatest common factor?? 5a2 35a The GCF is 5a

  6. What is the greatest common factor?? 7. 3y -8xy y 11x 8. 22x2 – 11x -x2 9. -4x6 - x4 - 2x2

  7. Factoring means to write as a product Always look for a Greatest Common Factor 1st. Factor 4x + 6y What is their greatest common factor? = 2( ) 2x + 3y Lets check. = 4x+6y =2(2x+3y)

  8. Factor 11. 3y – 8xy What is their GCF? = y( ) – 8x 3 12. 2a3 – 6ab2 = 2a( ) a2 – 3b2

  9. Factor 13. 2h2k + 2k What is their GCF? = 2k( ) + 1 h2 14. 6uv + 9v2 = 3v( ) 2u + 3v

  10. What if there is not GCF? 3x + 2 x2 + 3x + 2 Then it is prime Unless it is a trinomial, then I have to use another method.

  11. GCF • Factor: • xy – 5y • What is common? • Answer: y(x - 5) • What if we change the expression slightly? • x(x + 4) – 5(x + 4) • What is common? • Answer: (x + 4)(x – 5 )

  12. GCF • Try these: • 3x2 – 6x – 15x3 • 16x2 – 8x • y(y – 6) + 9(y – 6)

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