1. 8.1 – Monomials & Factoring

2. Factoring

3. Factoring – opposite of simplifying!

4. 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. 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. 133623141519

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. 133623141519 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. 133623141519 PC

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. 133623141519 PCP

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. 133623141519 PCPC

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. 133623141519 PCPCC

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. 133623141519 PCPCCP

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. 133623141519 PCPCCP *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. 133623141519 PCPCCP *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. 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 -1·2 2 ·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 -1·2 2 ·5·7

35. *greatest common factor (GCF)

36. - 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 2·2·3 2·2·2·2

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 2·2·2·22·2

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 2·2·2·22·2 = 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 2·2·2·22·2 = 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 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19

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 2·2·2·22·2 = 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 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/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 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2

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 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·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 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·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 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·x·y·y2·2·x·y

51. *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 2·2·2·22·2 = 4 b. 29 & 38 1·29 2·19N/A c. 36x 2 y & 56xy 2 2·2·3·3·x·x·y 2·2·2·7·x·y·y2·2·x·y = 4xy