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8.1 – Monomials & Factoring

8.1 – Monomials & Factoring. Factoring. Factoring – opposite of simplifying!. Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). Factoring – opposite of simplifying! Ex. Simplify 3(5) (7). 15 (7). Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7)

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8.1 – Monomials & Factoring

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  1. 8.1 – Monomials & Factoring

  2. Factoring

  3. Factoring – opposite of simplifying!

  4. Factoring – opposite of simplifying! Ex. Simplify 3(5)(7).

  5. Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7)

  6. Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105

  7. Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105 Ex. Factor 105.

  8. Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105 Ex. Factor 105. 15 · 7

  9. Factoring – opposite of simplifying! Ex. Simplify 3(5)(7). 15(7) 105 Ex. Factor 105. 15 · 7 3 · 5 · 7

  10. 2 Types of Numbers:

  11. 2 Types of Numbers: Prime

  12. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself

  13. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite

  14. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors

  15. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19

  16. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P

  17. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P C

  18. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P C P

  19. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P C P C

  20. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P C P C C

  21. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P C P C C P

  22. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P C P C C P *prime factorization

  23. 2 Types of Numbers: Prime – a whole number, greater than 1, whose only factors are 1 and itself Composite – a whole number, greater than 1, that has more than two factors Ex. 1 Classify each as prime or composite. 13 36 23 14 15 19 P C P C C P *prime factorization – when a whole number is expressed as the product of factors that are all prime numbers

  24. Ex. 2 Find the prime factorization of the following: a. 90

  25. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10

  26. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3

  27. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3 2·5

  28. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5

  29. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140

  30. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140

  31. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5

  32. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5

  33. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5 -1·22·5·7

  34. Ex. 2 Find the prime factorization of the following: a. 90 9 · 10 3·3·2·5 b. -140 -1 · 140 -1 · 14 · 10 -1 · 2·7 · 2·5 -1·22·5·7

  35. *greatest common factor (GCF)

  36. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression

  37. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression

  38. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16

  39. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·32·2·2·2

  40. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2

  41. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2

  42. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4

  43. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38

  44. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38 1·292·19

  45. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38 1·29 2·19

  46. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38 1·29 2·19 N/A

  47. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38 1·29 2·19 N/A c. 36x2y & 56xy2

  48. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38 1·29 2·19 N/A c. 36x2y & 56xy2 2·2·3·3·x·x·y2·2·2·7·x·y·y

  49. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38 1·29 2·19 N/A c. 36x2y & 56xy2 2·2·3·3·x·x·y2·2·2·7·x·y·y

  50. *greatest common factor (GCF) - the greatest number that is a factor of all numbers in the expression Ex. 3 Find the GCF of the following: a. 12 & 16 2·2·3 2·2·2·2 2·2 = 4 b. 29 & 38 1·29 2·19 N/A c. 36x2y & 56xy2 2·2·3·3·x·x·y2·2·2·7·x·y·y2·2·x·y

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