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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.