Factoring using the
Greatest Common Factor
      Module 10 - Topic 1
Factors
A factor is a number that divides evenly into
a number.


View this Cool Math website to review
factors. There is ...
Prime Factorization
A Prime number is divisible by 1 and itself.
Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
...
Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
...
Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
...
Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
...
Prime Factorization
A Prime number is divisible by 1 and itself.
Prime factorization are the prime factors that make up a
...
Finding & Factor GCF of a Polynomial
  View this 5 minute Prentice Hall video to learn how to find
  the GCF of a Polynomia...
Finding & Factor GCF of a Polynomial
  View this 5 minute Prentice Hall video to learn how to find
  the GCF of a Polynomia...
Finding & Factor GCF of a Polynomial
  View this 5 minute Prentice Hall video to learn how to find
  the GCF of a Polynomia...
Page 2 Try It
Factor:      2
           2x − 4x
Page 2 Try It
Factor:        2
             2x − 4x
          = 2x ⋅ x − 2x ⋅ 2
Page 2 Try It
Factor:        2
             2x − 4x
          = 2x ⋅ x − 2x ⋅ 2
Page 2 Try It
Factor:        2
             2x − 4x
          = 2x ⋅ x − 2x ⋅ 2


          = 2x ( x − 2 )
Page 2 Try It
Factor:        2
             2x − 4x
          = 2x ⋅ x − 2x ⋅ 2


          = 2x ( x − 2 )
Page 2 Try It
Factor:        2
             2x − 4x
          = 2x ⋅ x − 2x ⋅ 2


          = 2x ( x − 2 )
Page 2 Try It
Factor:     7x + 14x   2
Page 2 Try It
Factor:       7x + 14x   2



          = 7x ⋅1 + 7x ⋅ 2x
Page 2 Try It
Factor:       7x + 14x   2



          = 7x ⋅1 + 7x ⋅ 2x
Page 2 Try It
Factor:       7x + 14x     2



          = 7x ⋅1 + 7x ⋅ 2x


          = 7x (1 + 2x )
Page 2 Try It
Factor:       7x + 14x     2



          = 7x ⋅1 + 7x ⋅ 2x


          = 7x (1 + 2x )
Page 2 Try It
Factor:       7x + 14x     2



          = 7x ⋅1 + 7x ⋅ 2x


          = 7x (1 + 2x )
Page 4 Your Turn
Factor:      2   4   3     3 3     5    7
          15a b − 5ab + 20a b + 10a b
Page 4 Your Turn
Factor:          2   4       3       3 3       5   7
              15a b − 5ab + 20a b + 10a b

         ...
Page 4 Your Turn
Factor:          2   4       3       3 3       5   7
              15a b − 5ab + 20a b + 10a b

         ...
Page 4 Your Turn
Factor:                2   4       3           3 3               5   7
              15a b − 5ab + 20a b ...
Page 4 Your Turn
Factor:
            4   3   2 2   5 6
          6x y + 2x y − 8x y
Page 4 Your Turn
Factor:
                 4   3     2 2   5 6
            6x y + 2x y − 8x y
      2 2    2           2 2 ...
Page 4 Your Turn
Factor:
                 4   3     2 2   5 6
            6x y + 2x y − 8x y
      2 2    2           2 2 ...
Page 4 Your Turn
Factor:
                        4       3     2 2         5 6
                6x y + 2x y − 8x y
      2 ...
Factor.
          5    3 3      2 2
      5x y + 25x y − 15x y
Answer:         2
                    (   3   2
            5x y x + 5xy − 3x y 2
                                    )
He...
Answer:        2
                     (   3
             5x y x + 5xy − 3x y     2       2
                               ...
Answer:           2
                        (   3
                5x y x + 5xy − 3x y     2       2
                      ...
Answer:           2
                        (   3
                5x y x + 5xy − 3x y     2       2
                      ...
Answer:           2
                        (   3
                5x y x + 5xy − 3x y     2       2
                      ...
Answer:           2
                        (   3
                5x y x + 5xy − 3x y     2       2
                      ...
Factor:
          8 3   5 5       8
    12d e − 18d e − 27e
Answer:          3
                     (   8   5 2
                3e 4d − 6d e − 9e   5
                                ...
Answer:        3
                     (   8   5 2
                3e 4d − 6d e − 9e            5
                         ...
Answer:         3
                      (   8   5 2
                 3e 4d − 6d e − 9e            5
                      ...
Answer:         3
                      (   8   5 2
                 3e 4d − 6d e − 9e            5
                      ...
Answer:         3
                      (   8   5 2
                 3e 4d − 6d e − 9e            5
                      ...
Answer:         3
                      (   8   5 2
                 3e 4d − 6d e − 9e            5
                      ...
Factor:
             12    8        5
          14a − 28a + 14a
Answer:            5
                       (   7
                14a a − 2a + 1 3
                                   )
He...
Answer:          5
                       (
                14a a − 2a + 1 7           3
                                 ...
Answer:          5
                       (
                14a a − 2a + 1 7           3
                                 ...
Answer:          5
                       (
                14a a − 2a + 1 7           3
                                 ...
Answer:          5
                       (
                14a a − 2a + 1 7           3
                                 ...
Answer:          5
                       (
                14a a − 2a + 1 7           3
                                 ...
Great Job!
You’ve finished reviewing Factoring with a GCF notes.
Exit and proceed to the Mastery Assignment.
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Module 10 Topic 1 factoring gcf

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  • Module 10 Topic 1 factoring gcf

    1. 1. Factoring using the Greatest Common Factor Module 10 - Topic 1
    2. 2. Factors A factor is a number that divides evenly into a number. View this Cool Math website to review factors. There is only the 1 page to review.
    3. 3. Prime Factorization A Prime number is divisible by 1 and itself.
    4. 4. Prime Factorization A Prime number is divisible by 1 and itself. Prime factorization are the prime factors that make up a number.
    5. 5. Prime Factorization A Prime number is divisible by 1 and itself. Prime factorization are the prime factors that make up a number. Every number has a unique prime factorization.
    6. 6. Prime Factorization A Prime number is divisible by 1 and itself. Prime factorization are the prime factors that make up a number. Every number has a unique prime factorization. Such as the prime factorization of 2 2 A) 36 = 2 ⋅ 2 ⋅ 3 ⋅ 3 or 2 ⋅ 3
    7. 7. Prime Factorization A Prime number is divisible by 1 and itself. Prime factorization are the prime factors that make up a number. Every number has a unique prime factorization. Such as the prime factorization of 2 2 A) 36 = 2 ⋅ 2 ⋅ 3 ⋅ 3 or 2 ⋅ 3 B) 105 = 3 ⋅ 5 ⋅ 7
    8. 8. Prime Factorization A Prime number is divisible by 1 and itself. Prime factorization are the prime factors that make up a number. Every number has a unique prime factorization. Such as the prime factorization of 2 2 A) 36 = 2 ⋅ 2 ⋅ 3 ⋅ 3 or 2 ⋅ 3 B) 105 = 3 ⋅ 5 ⋅ 7 If you do not remember how to find the prime factorization of a number, Purple Math will help you review Prime Factorization here.
    9. 9. Finding & Factor GCF of a Polynomial View this 5 minute Prentice Hall video to learn how to find the GCF of a Polynomial.
    10. 10. Finding & Factor GCF of a Polynomial View this 5 minute Prentice Hall video to learn how to find the GCF of a Polynomial.
    11. 11. Finding & Factor GCF of a Polynomial View this 5 minute Prentice Hall video to learn how to find the GCF of a Polynomial. Now view this Cool Math website to learn how to factor the GCF from a polynomial. There are 4 pages to review. Be sure to do the Try It and Your Turn problems in your notebook. Check your answers on the following slides.
    12. 12. Page 2 Try It Factor: 2 2x − 4x
    13. 13. Page 2 Try It Factor: 2 2x − 4x = 2x ⋅ x − 2x ⋅ 2
    14. 14. Page 2 Try It Factor: 2 2x − 4x = 2x ⋅ x − 2x ⋅ 2
    15. 15. Page 2 Try It Factor: 2 2x − 4x = 2x ⋅ x − 2x ⋅ 2 = 2x ( x − 2 )
    16. 16. Page 2 Try It Factor: 2 2x − 4x = 2x ⋅ x − 2x ⋅ 2 = 2x ( x − 2 )
    17. 17. Page 2 Try It Factor: 2 2x − 4x = 2x ⋅ x − 2x ⋅ 2 = 2x ( x − 2 )
    18. 18. Page 2 Try It Factor: 7x + 14x 2
    19. 19. Page 2 Try It Factor: 7x + 14x 2 = 7x ⋅1 + 7x ⋅ 2x
    20. 20. Page 2 Try It Factor: 7x + 14x 2 = 7x ⋅1 + 7x ⋅ 2x
    21. 21. Page 2 Try It Factor: 7x + 14x 2 = 7x ⋅1 + 7x ⋅ 2x = 7x (1 + 2x )
    22. 22. Page 2 Try It Factor: 7x + 14x 2 = 7x ⋅1 + 7x ⋅ 2x = 7x (1 + 2x )
    23. 23. Page 2 Try It Factor: 7x + 14x 2 = 7x ⋅1 + 7x ⋅ 2x = 7x (1 + 2x )
    24. 24. Page 4 Your Turn Factor: 2 4 3 3 3 5 7 15a b − 5ab + 20a b + 10a b
    25. 25. Page 4 Your Turn Factor: 2 4 3 3 3 5 7 15a b − 5ab + 20a b + 10a b 3 3 3 2 3 4 4 = 5ab ⋅ 3ab − 5ab ⋅1 + 5ab ⋅ 4a + 5ab ⋅ 2a b
    26. 26. Page 4 Your Turn Factor: 2 4 3 3 3 5 7 15a b − 5ab + 20a b + 10a b 3 3 3 2 3 4 4 = 5ab ⋅ 3ab − 5ab ⋅1 + 5ab ⋅ 4a + 5ab ⋅ 2a b
    27. 27. Page 4 Your Turn Factor: 2 4 3 3 3 5 7 15a b − 5ab + 20a b + 10a b 3 3 3 2 3 4 4 = 5ab ⋅ 3ab − 5ab ⋅1 + 5ab ⋅ 4a + 5ab ⋅ 2a b 3 ( = 5ab 3ab − 1 + 4a + 2a b 2 4 4 )
    28. 28. Page 4 Your Turn Factor: 4 3 2 2 5 6 6x y + 2x y − 8x y
    29. 29. Page 4 Your Turn Factor: 4 3 2 2 5 6 6x y + 2x y − 8x y 2 2 2 2 2 2 2 3 4 = 2x y ⋅ 3x y + 2x y ⋅1 − 2x y ⋅ 4x y
    30. 30. Page 4 Your Turn Factor: 4 3 2 2 5 6 6x y + 2x y − 8x y 2 2 2 2 2 2 2 3 4 = 2x y ⋅ 3x y + 2x y ⋅1 − 2x y ⋅ 4x y
    31. 31. Page 4 Your Turn Factor: 4 3 2 2 5 6 6x y + 2x y − 8x y 2 2 2 2 2 2 2 3 4 = 2x y ⋅ 3x y + 2x y ⋅1 − 2x y ⋅ 4x y 2 2 ( = 2x y 3x y + 1 − 4x y 2 3 4 )
    32. 32. Factor. 5 3 3 2 2 5x y + 25x y − 15x y
    33. 33. Answer: 2 ( 3 2 5x y x + 5xy − 3x y 2 ) Here’s how...
    34. 34. Answer: 2 ( 3 5x y x + 5xy − 3x y 2 2 ) Here’s how... 5 3 3 2 2 5x y + 25x y − 15x y 5 5x y = 5 x x x x x y 3 3 25x y = 5 5 x x x y y y 2 2 −15x y = −1 5 3 x x y y
    35. 35. Answer: 2 ( 3 5x y x + 5xy − 3x y 2 2 ) Here’s how... 5 3 3 2 2 5x y + 25x y − 15x y 5 5x y = 5 x x x x x y 3 3 25x y = 5 5 x x x y y y 2 2 −15x y = −1 5 3 x x y y 2 GCF: 5x y
    36. 36. Answer: 2 ( 3 5x y x + 5xy − 3x y 2 2 ) Here’s how... 5 3 3 2 2 5x y + 25x y − 15x y 5 5x y = 5 x x x x x y 3 3 25x y = 5 5 x x x y y y 2 2 −15x y = −1 5 3 x x y y 2 GCF: 5x y
    37. 37. Answer: 2 ( 3 5x y x + 5xy − 3x y 2 2 ) Here’s how... 5 3 3 2 2 5x y + 25x y − 15x y 5 5x y = 5 x x x x x y 3 3 25x y = 5 5 x x x y y y 2 2 −15x y = −1 5 3 x x y y 2 GCF: 5x y
    38. 38. Answer: 2 ( 3 5x y x + 5xy − 3x y 2 2 ) Here’s how... 5 3 3 2 2 5x y + 25x y − 15x y 5 5x y = 5 x x x x x y 3 3 25x y = 5 5 x x x y y y 2 2 −15x y = −1 5 3 x x y y 2 GCF: 5x y
    39. 39. Factor: 8 3 5 5 8 12d e − 18d e − 27e
    40. 40. Answer: 3 ( 8 5 2 3e 4d − 6d e − 9e 5 ) Here’s how...
    41. 41. Answer: 3 ( 8 5 2 3e 4d − 6d e − 9e 5 ) Here’s how... 8 3 5 5 8 12d e − 18d e − 27e 8 3 12d e = 2 2 3 d 5 d 3 e 3 5 5 −18d e = −1 2 3 3 d 5 e 3 e 2 8 3 5 −27e = −1 3 3 3 e e
    42. 42. Answer: 3 ( 8 5 2 3e 4d − 6d e − 9e 5 ) Here’s how... 8 3 5 5 8 12d e − 18d e − 27e 8 3 12d e = 2 2 3 d 5 d 3 e 3 5 5 −18d e = −1 2 3 3 d 5 e 3 e 2 8 3 5 −27e = −1 3 3 3 e e 3 GCF: 3e
    43. 43. Answer: 3 ( 8 5 2 3e 4d − 6d e − 9e 5 ) Here’s how... 8 3 5 5 8 12d e − 18d e − 27e 8 3 12d e = 2 2 3 d 5 d 3 e 3 5 5 −18d e = −1 2 3 3 d 5 e 3 e 2 8 3 5 −27e = −1 3 3 3 e e 3 GCF: 3e
    44. 44. Answer: 3 ( 8 5 2 3e 4d − 6d e − 9e 5 ) Here’s how... 8 3 5 5 8 12d e − 18d e − 27e 8 3 12d e = 2 2 3 d 5 d 3 e 3 5 5 −18d e = −1 2 3 3 d 5 e 3 e 2 8 3 5 −27e = −1 3 3 3 e e 3 GCF: 3e
    45. 45. Answer: 3 ( 8 5 2 3e 4d − 6d e − 9e 5 ) Here’s how... 8 3 5 5 8 12d e − 18d e − 27e 8 3 12d e = 2 2 3 d 5 d 3 e 3 5 5 −18d e = −1 2 3 3 d 5 e 3 e 2 8 3 5 −27e = −1 3 3 3 e e 3 GCF: 3e
    46. 46. Factor: 12 8 5 14a − 28a + 14a
    47. 47. Answer: 5 ( 7 14a a − 2a + 1 3 ) Here’s how...
    48. 48. Answer: 5 ( 14a a − 2a + 1 7 3 ) Here’s how... 12 8 5 14a − 28a + 21a 12 14a = 2 7 a 5 a 7 8 5 3 −28a = −1 2 2 7 a a 5 5 21a = 2 7 a
    49. 49. Answer: 5 ( 14a a − 2a + 1 7 3 ) Here’s how... 12 8 5 14a − 28a + 21a 12 14a = 2 7 a 5 a 7 8 5 3 −28a = −1 2 2 7 a a 5 5 21a = 2 7 a 5 GCF: 14a
    50. 50. Answer: 5 ( 14a a − 2a + 1 7 3 ) Here’s how... 12 8 5 14a − 28a + 21a 12 14a = 2 7 a 5 a 7 8 5 3 −28a = −1 2 2 7 a a 5 5 21a = 2 7 a 5 GCF: 14a
    51. 51. Answer: 5 ( 14a a − 2a + 1 7 3 ) Here’s how... 12 8 5 14a − 28a + 21a 12 14a = 2 7 a 5 a 7 8 5 3 −28a = −1 2 2 7 a a 5 5 21a = 2 7 a 5 GCF: 14a
    52. 52. Answer: 5 ( 14a a − 2a + 1 7 3 ) Here’s how... 12 8 5 14a − 28a + 21a 12 14a = 2 7 a 5 a 7 8 5 3 −28a = −1 2 2 7 a a 5 5 21a = 2 7 a No factors but there is an imaginary 1 5 GCF: 14a
    53. 53. Great Job! You’ve finished reviewing Factoring with a GCF notes. Exit and proceed to the Mastery Assignment.

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