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# 6.3 gcf factoring

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### 6.3 gcf factoring

1. 1. Drill Distribute and simplify: 1) (2x – 1)(3x + 5) 2) (x + 1)2 =
2. 2. Objective • SWBAT factor polynomials by finding the greatest common factor.
3. 3. GCF • The greatest common factor of a set of numbers is the largest number that divides evenly into all the numbers in that set.
4. 4. GCF • We need to be able to do this for 2 or 3 numbers. • If the numbers are relatively prime the GCF is one.
5. 5. Examples Find the GCF for the numbers listed below: 12, 20
6. 6. Examples Find the GCF for the numbers listed below: 8, 64
7. 7. Examples Find the GCF for the numbers listed below: 14, 56
8. 8. Examples Find the GCF for the numbers listed below: 40, 21
9. 9. Examples Find the GCF for the numbers listed below: 10, 12, 20
10. 10. Examples Find the GCF for the numbers listed below: 24, 16, 30
11. 11. Warm UP 1. Use a factor Tree to find the prime factorization of 120. 2. Find the GCF: 40, 25 3. Find the GCF: 36, 24, 60
12. 12. Objective • SWBAT factor polynomials using the GCF.
13. 13. With Variables Involved • When you have variables in your terms you will do the number things just like we did. For the variables simply take the least amount of each one.
14. 14. Examples Find the GCF for the terms listed below: 2 4x , 4 10x
15. 15. Examples Find the GCF for the terms listed below: 4, 9m3 46m
16. 16. Examples Find the GCF for the terms listed below: 3, 6x2, 2x 8 10x
17. 17. Examples Find the GCF for the terms listed below: 2, 12y, 9y 2 18y
18. 18. Factoring 2 12x – 15x 
19. 19. Factoring 2 12x – 15x  3x (4x – 5)
20. 20. So… • For each polynomial you will first need to determine the GCF. • Then each terms is divided by the GCF to find the part in the parenthesis.
21. 21. Example • Factor: 2 3x + 6x =
22. 22. Example • Factor: 2 16x + 4x =
23. 23. Example • Factor: 2 6x + 26 =
24. 24. Example • Factor: 4 3y – 3 12y + 2 9y =
25. 25. Example • Factor: 3 2x – 2 6x + 8x =
26. 26. Example • Factor: 7 100x + 6 20x + 5= 50x
27. 27. Drill Distribute and simplify: 1) (2x – 1)(3x + 5) 2) (x + 1)2 =
28. 28. GCF • The greatest common factor of a set of numbers is the largest number that divides evenly into all the numbers in that set.
29. 29. GCF • We need to be able to do this for 2 or 3 numbers. • If the numbers are relatively prime the GCF is one.
30. 30. Examples Find the GCF for the numbers listed below: 12, 20
31. 31. Examples Find the GCF for the numbers listed below: 8, 64
32. 32. Examples Find the GCF for the numbers listed below: 14, 56
33. 33. Examples Find the GCF for the numbers listed below: 40, 21
34. 34. Examples Find the GCF for the numbers listed below: 10, 12, 20
35. 35. Examples Find the GCF for the numbers listed below: 24, 16, 30
36. 36. With Variables Involved • When you have variables in your terms you will do the number things just like we did. For the variables simply take the least amount of each one.
37. 37. Examples Find the GCF for the terms listed below: 2 4x , 4 10x
38. 38. Examples Find the GCF for the terms listed below: 4, 9m3 46m
39. 39. Examples Find the GCF for the terms listed below: 3, 6x2, 2x 8 10x
40. 40. Examples Find the GCF for the terms listed below: 2, 12y, 9y 2 18y
41. 41. Factoring 2 12x – 15x 
42. 42. So… • For each polynomial you will first need to determine the GCF. • Then each terms is divided by the GCF to find the part in the parenthesis.
43. 43. Example • Factor: 2 3x + 6x =
44. 44. Example • Factor: 2 16x + 4x =
45. 45. Example • Factor: 2 6x + 26 =
46. 46. Example • Factor: 4 3y – 3 12y + 2 9y =
47. 47. Example • Factor: 3 2x – 2 6x + 8x =
48. 48. Example • Factor: 7 100x + 6 20x + 5= 50x