Your SlideShare is downloading.
×

×

Saving this for later?
Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.

Text the download link to your phone

Standard text messaging rates apply

Like this presentation? Why not share!

- 2 4linear word problems by math123a 534 views
- 5 2factoring trinomial i by math123a 736 views
- A9factoring out gcf by elealgreview 55 views
- 1 1 review on factoring by math123b 959 views
- 6.3 gcf factoring day 2 by jbianco9910 120 views
- March 19, 2014 by khyps13 480 views
- 6.3 gcf factoring by jbianco9910 56 views
- Factroring gcf by gkadien 173 views
- Factoring Polynomials by itutor 931 views
- Factoring Polynomials by Ver Louie Gautani 2196 views
- March 18, 2014 by khyps13 526 views
- Math083 day 1 chapter 6 2013 fall by jbianco9910 135 views

545

Published on

No Downloads

Total Views

545

On Slideshare

0

From Embeds

0

Number of Embeds

0

Shares

0

Downloads

0

Comments

0

Likes

1

No embeds

No notes for slide

- 1. Factoring Out GCF
- 2. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way).
- 3. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime.
- 4. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime.
- 5. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely.
- 6. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2
- 7. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime, incomplete factored completely
- 8. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities.
- 9. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5,
- 10. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor.
- 11. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are
- 12. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2,
- 13. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a,
- 14. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a, 2a.
- 15. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a, 2a. c. The common factors of 6xy2, 15x2y2 are
- 16. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a, 2a. c. The common factors of 6xy2, 15x2y2 are 3,
- 17. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a, 2a. c. The common factors of 6xy2, 15x2y2 are 3, x,
- 18. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a, 2a. c. The common factors of 6xy2, 15x2y2 are 3, x, y2,
- 19. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a, 2a. c. The common factors of 6xy2, 15x2y2 are 3, x, y2, xy2, ..
- 20. Factoring Out GCF To factor means to rewrite a quantity as a product (in a nontrivial way). A quantity x that can’t be written as product besides as 1*x is said to be prime. To factor completely means each factor in the product is prime. Example A. Factor 12 completely. 12 = 3 * 4 = 3 * 2 * 2 not prime factored completely A common factor of two or more quantities is a factor belongs to all the quantities. Example B. a. Sincer 6 = 2*3, 15 = 3*5, 3 is a common factor. b. The common factor of 4ab, 6a are 2, a, 2a. c. The common factors of 6xy2, 15x2y2 are 3, x, y2, xy2, .. d. The common factor of a(x+y), b(x+y) is (x+y).
- 21. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors.
- 22. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36}
- 23. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12.
- 24. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a}
- 25. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a.
- 26. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a. c. GCF {6xy2, 15 x2y2}
- 27. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a. c. GCF {6xy2, 15 x2y2} = 3xy2.
- 28. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a. c. GCF {6xy2, 15 x2y2} = 3xy2. d. GCF{x3y5, x4y6, x5y4} =
- 29. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a. c. GCF {6xy2, 15 x2y2} = 3xy2. d. GCF{x3y5, x4y6, x5y4} = x3y4.
- 30. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a. c. GCF {6xy2, 15 x2y2} = 3xy2. d. GCF{x3y5, x4y6, x5y4} = x3y4. The Extraction Law Distributive law interpreted backward gives the Extraction Law, that is, common factors may be extracted from sums or differences.
- 31. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a. c. GCF {6xy2, 15 x2y2} = 3xy2. d. GCF{x3y5, x4y6, x5y4} = x3y4. The Extraction Law Distributive law interpreted backward gives the Extraction Law, that is, common factors may be extracted from sums or differences. AB ± AC  A(B±C)
- 32. Factoring Out GCF The greatest common factor (GCF) is the common factor that has the largest coefficient and highest degree of each factor among all common factors. Example C. Find the GCF of the given quantities. a. GCF{24, 36} = 12. b. GCF{4ab, 6a} = 2a. c. GCF {6xy2, 15 x2y2} = 3xy2. d. GCF{x3y5, x4y6, x5y4} = x3y4. The Extraction Law Distributive law interpreted backward gives the Extraction Law, that is, common factors may be extracted from sums or differences. AB ± AC  A(B±C) This procedure is also called “factoring out a common factor”. To factor, the first step always is to factor out the GCF.
- 33. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y
- 34. (the GCF is y) Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y
- 35. (the GCF is y) Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4)
- 36. (the GCF is y) Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) b. 4ab + 6a
- 37. (the GCF is y) (the GCF is 2a) Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) b. 4ab + 6a
- 38. (the GCF is y) (the GCF is 2a) Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) b. 4ab + 6a = 2a(2b) + 2a(3)
- 39. (the GCF is y) (the GCF is 2a) Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3)
- 40. (the GCF is y) (the GCF is 2a) Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) c. 12x2y3 + 6x2y2
- 41. Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) Factoring Out GCF c. 12x2y3 + 6x2y2 (the GCF is 6x2y2)
- 42. Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) Factoring Out GCF c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) (the GCF is 6x2y2)
- 43. Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) Factoring Out GCF c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2)
- 44. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2) We may pull out common factors that are ( )'s.
- 45. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2) We may pull out common factors that are ( )'s. Example E. Factor a. a(x + y) – 4(x + y)
- 46. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2) We may pull out common factors that are ( )'s. Example E. Factor a. a(x + y) – 4(x + y) Pull out the common factor (x + y)
- 47. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2) We may pull out common factors that are ( )'s. Example E. Factor a. a(x + y) – 4(x + y) Pull out the common factor (x + y) a(x + y) – 4(x + y) = (x + y)(a – 4)
- 48. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2) We may pull out common factors that are ( )'s. Example E. Factor a. a(x + y) – 4(x + y) Pull out the common factor (x + y) a(x + y) – 4(x + y) = (x + y)(a – 4) b. Factor (2x – 3)3x – 2(2x – 3)
- 49. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2) We may pull out common factors that are ( )'s. Example E. Factor a. a(x + y) – 4(x + y) Pull out the common factor (x + y) a(x + y) – 4(x + y) = (x + y)(a – 4) b. Factor (2x – 3)3x – 2(2x – 3) Pull out the common factor (2x – 3),
- 50. Factoring Out GCF Example D. Factor out the GCF. a. xy – 4y = y(x – 4) (the GCF is y) b. 4ab + 6a = 2a(2b) + 2a(3) = 2a(2b + 3) (the GCF is 2a) c. 12x2y3 + 6x2y2 = 6x2y2(2y) + 6x2y2(1) = 6x2y2(2y + 1) (the GCF is 6x2y2) We may pull out common factors that are ( )'s. Example E. Factor a. a(x + y) – 4(x + y) Pull out the common factor (x + y) a(x + y) – 4(x + y) = (x + y)(a – 4) b. Factor (2x – 3)3x – 2(2x – 3) Pull out the common factor (2x – 3), (2x – 3)3x – 2(2x – 3) = (2x – 3)(3x – 2)
- 51. Factoring Out GCF We sometimes pull out a negative sign from an expression.
- 52. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5.
- 53. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5)
- 54. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice.
- 55. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice. Example G. Factor by pulling out twice. a. y(2x – 5) – 2x + 5
- 56. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice. Example G. Factor by pulling out twice. a. y(2x – 5) – 2x + 5 = y(2x – 5) – (2x – 5)
- 57. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice. Example G. Factor by pulling out twice. a. y(2x – 5) – 2x + 5 = y(2x – 5) – (2x – 5) = (2x – 5)(y – 1)
- 58. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice. Example G. Factor by pulling out twice. a. y(2x – 5) – 2x + 5 = y(2x – 5) – (2x – 5) = (2x – 5)(y – 1) b. 3x – 3y + ax – ay
- 59. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice. Example G. Factor by pulling out twice. a. y(2x – 5) – 2x + 5 = y(2x – 5) – (2x – 5) = (2x – 5)(y – 1) b. 3x – 3y + ax – ay Group them into two groups. = (3x – 3y) + (ax – ay)
- 60. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice. Example G. Factor by pulling out twice. a. y(2x – 5) – 2x + 5 = y(2x – 5) – (2x – 5) = (2x – 5)(y – 1) b. 3x – 3y + ax – ay Group them into two groups. = (3x – 3y) + (ax – ay) Factor out the GCF of each group. = 3(x – y) + a(x – y)
- 61. Factoring Out GCF We sometimes pull out a negative sign from an expression. Example F. Pull out the negative sign from –2x + 5. –2x + 5 = –(2x – 5) Sometime we have to use factor twice. Example G. Factor by pulling out twice. a. y(2x – 5) – 2x + 5 = y(2x – 5) – (2x – 5) = (2x – 5)(y – 1) b. 3x – 3y + ax – ay Group them into two groups. = (3x – 3y) + (ax – ay) Factor out the GCF of each group. = 3(x – y) + a(x – y) Pull the factor (x – y) again. = (3 + a)(x – y)

Be the first to comment