1. 5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9) 2. (-2x - 1) - (x - 7) 3. (9x + 5) - (6x - 8) 4. (-8x + 1) - (8x - 1)

2. 5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9)

3. 5 Minute Check Simplify each expression. Complete in your notes. 1. (-3x - 2) - (7x + 9) -3x - 2 - 7x - 9 -10x - 11

4. 5 Minute Check Simplify each expression. Complete in your notes. 2. (-2x - 1) - (x - 7)

5. 5 Minute Check Simplify each expression. Complete in your notes. 2. (-2x - 1) - (x - 7) -2x - 1 - x + 7 -3x + 6

6. 5 Minute Check Simplify each expression. Complete in your notes. 3. (9x + 5) - (6x - 8)

7. 5 Minute Check Simplify each expression. Complete in your notes. 3. (9x + 5) - (6x - 8) 9x + 5 - 6x + 8 3x + 13

8. 5 Minute Check Simplify each expression. Complete in your notes. 4. (-8x + 1) - (8x - 1)

9. 5 Minute Check Simplify each expression. Complete in your notes. 4. (-8x + 1) - (8x - 1) -8x + 1 - 8x + 1 -16x + 2

10. Monday, May 18 Lesson 7.5.8 Factor Linear Expressions

11. Objective: To use properties of mathematics to factor linear expressions.

12. Factor Linear Expressions A monomial is a number, a variable, or a product of a number and one or more variables. Monomials; 25, x, 25x Not Monomials: x + 25, 25x + 100

13. Factor Linear Expressions To factor a number means to write it as a product of its prime factors. 36; 2 · 2 · 3 · 3

14. Factor Linear Expressions A linear algebraic expression can be factored using the same method you would use to factor a number.

15. Factor Linear Expressions Factor the expression. 12 + 30x How to Factor Monomials. (Method 1) Step 1 – Write both monomials as prime factors.

16. Factor Linear Expressions Factor the expression. 12 + 30x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 1 – Write both monomials as prime factors.

17. Factor Linear Expressions Factor the expression. 12 + 30x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 2 – Circle the common factors.

18. Factor Linear Expressions Factor the expression. 12 + 30x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 2 – Circle the common factors.

19. Factor Linear Expressions Factor the expression. 12 + 30x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x How to Factor Monomials. Step 3 – Find the GCF by multiplying the common factors for one number.

20. Factor Linear Expressions Factor the expression. 12 + 30x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x GCF = 2 · 3 = 6 How to Factor Monomials. Step 3 – Find the GCF by multiplying the common factors for one number.

21. Factor Linear Expressions Factor the expression. 12 + 30x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x GCF = 2 · 3 = 6 How to Factor Monomials. Step 4 – Rewrite the expression with the GCF outside the parenthesis. 3 0: 2 · 3 · 5 · x

22. Factor Linear Expressions Factor the expression. 12 + 30x 12: 2 · 2 · 3 30: 2 · 3 · 5 · x GCF = 2 · 3 = 6 6(2 + 5x) How to Factor Monomials. Step 4 – Rewrite the expression with the GCF outside the parenthesis.

23. Factor Linear Expressions Factor the expression. 8 + 12x Step 1 – ?

24. Factor Linear Expressions Factor the expression. 8 + 12x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x Step 2 – ?

25. Factor Linear Expressions Factor the expression. 8 + 12x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x Step 3 –

26. Factor Linear Expressions Factor the expression. 8 + 12x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x The GCF is 2 · 2, or 4 Step 4 –

27. Factor Linear Expressions Factor the expression. 8 + 12x 8 = 2 · 2 · 2 12x = 2 · 2 · 3 · x The GCF is 2 · 2, or 4 4(2 + 3x)

28. Factor Linear Expressions Factor the expression. 18a + 20ab How to Factor Monomials. (Method 2) Step 1 – Factor out any common variables.

29. Factor Linear Expressions Factor the expression. 18a + 20ab a(18 + 20b) How to Factor Monomials. (Method 2) Step 1 – Factor out any common variables.

30. Factor Linear Expressions Factor the expression. 18a + 20ab a(18 + 20b) How to Factor Monomials. (Method 2) Step 2 – Factor out 2, if possible, and keep factoring until you can’t.

31. Factor Linear Expressions Factor the expression. 18a + 20ab a(18 + 20b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 2 – Factor out 2, if possible, and keep factoring until you can’t.

32. Factor Linear Expressions Factor the expression. 18a + 20ab a(18 + 20b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 3 – Factor out 3, if possible, and keep factoring until you can’t.

33. Factor Linear Expressions Factor the expression. 18a + 20ab a(18 + 20b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 3 – Factor out 3, if possible, and keep factoring until you can’t.

34. Factor Linear Expressions Factor the expression. 18a + 20ab a(18 + 20b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 4 – Factor out any remaining prime numbers, if possible.

35. Factor Linear Expressions Factor the expression. 18a + 20ab a(18 + 20b) 2a(9 + 10b) How to Factor Monomials. (Method 2) Step 4 – Factor out any remaining prime numbers, if possible.

36. Factor Linear Expressions Factor the expression. 12 + 28c Step 1 - ? (Method 2)

37. Factor Linear Expressions Factor the expression. 12 + 28c Step 2 - ? (Method 2)

38. Factor Linear Expressions Factor the expression. 12 + 28c 2(6 + 14c) 4(3 + 7c) Step 3 - ? (Method 2)

39. Factor Linear Expressions Factor the expression. 12 + 28c 2(6 + 14c) 4(3 + 7c) Step 4 - ? (Method 2)

40. Factor Linear Expressions Factor the expression. 12 + 28c 2(6 + 14c) 4(3 + 7c)

41. Factor Linear Expressions Factor the expression. 25x + 15xy Do this on your own.

42. Factor Linear Expressions Factor the expression. Method 1 25x + 15xy 25x = 5 · 5 · x 15xy = 3 · 5 · x · y The GCF is 5 · x, or 5x 5x (5 + 3y)

43. Factor Linear Expressions Factor the expression. Method 2 25x + 15xy x(25 + 15y) 5x (5 + 3y)

44. Factor Linear Expressions Factor the expression. 42mn + 14n Do this on your own.

45. Factor Linear Expressions Factor the expression. Method 1 42mn + 14n 42mn = 2 · 3 · 7 · m · n 14n = 2 · 7 · n The GCF is 2 · 7 · n, or 14n 14n(3m + 1)

46. Factor Linear Expressions Factor the expression. Method 2 42mn + 14n n(42m + 14) 2n(21m + 7) 14n(3m + 1)

47. Factor Linear Expressions Factor the expression. 3x + 9

48. Factor Linear Expressions Factor the expression. Method 1 3x + 9 3x = 3 · x 9 = 3 · 3 The GCF is 3 3(x + 3)

49. Factor Linear Expressions Factor the expression. Method 2 3x + 9 3(x + 3)

50. Factor Linear Expressions Factor the expression. 12x + 7y

51. Factor Linear Expressions Factor the expression. 12x + 7y 12x = 2 · 2 · 3 · x 7y = 7 · y The are no common factors, the expression cannot be factored.

52. Factor Linear Expressions Factor the expression. 4x - 28

53. Factor Linear Expressions Factor the expression. Method 1 4x - 28 4x = 2 · 2 · x 28 = 2 · 2 · 7 The GCF is 4 4(x - 7)

54. Factor Linear Expressions Factor the expression. Method 2 4x - 28 2(2x – 14) 4(x - 7)

55. Factor Linear Expressions Factor the expression. 3x + 33y

56. Factor Linear Expressions Factor the expression. Method 1 3x + 33y 3x = 3 · x 33y = 3 · 11 · y The GCF is 3 3(x + 11y)

57. Factor Linear Expressions Factor the expression. Method 2 3x + 33y 3(x + 11y)

58. Factor Linear Expressions Factor the expression. 4x + 35

59. Factor Linear Expressions Factor the expression. 4x + 35 4x = 2 · 2 · x 35 = 5 · 7 There is no GCF and cannot be factored.

60. Factor Linear Expressions Factor the expression. 32x + 18

61. Factor Linear Expressions Factor the expression. Method 1 32x + 18 32x = 2 · 2 · 2 · 2 · 2 · x 18 = 2 · 3 · 3 The GCF is 2 2(16x + 9)

62. Factor Linear Expressions Factor the expression. Method 2 32x + 18 2(16x + 9)

63. Factor Linear Expressions Factor the expression. 27s – 54st

64. Factor Linear Expressions Factor the expression. Method 1 27s – 54st 27s = 3 · 3 · 3 · s 54st = 2 · 3 · 3 · 3 · s · t The GCF is 27s 27s(1 – 2t)

65. Factor Linear Expressions Factor the expression. Method 2 27s – 54st s(27 – 54t) 3s(9 – 18t) 9s(3 – 6t) 27s(1 – 2t)

66. Factor Linear Expressions Factor the expression. 18cd + 30d

67. Factor Linear Expressions Factor the expression. Method 1 18cd + 30d 18cd = 2 · 3 · 3 · c · d 30d = 2 · 3 · 5 · d The GCF is 6d 6d(3c + 5)

68. Factor Linear Expressions Factor the expression. Method 2 18cd + 30d d(18c + 30) 2d(9c + 15) 6d(3c + 5)

69. Factor Linear Expressions Factor the expression. 36x + 24

70. Factor Linear Expressions Factor the expression. Method 1 36x + 24 36x = 2 · 2 · 3 · 3 · x 24 = 2 · 2 · 2 · 3 The GCF is 12 12(3x + 2)

71. Factor Linear Expressions Factor the expression. Method 2 36x + 24 2(18x + 12) 4(9x + 6) 12(3x + 2)

72. Factor Linear Expressions Factor the expression. 4x + 9

73. Factor Linear Expressions Factor the expression. 4x + 9 x = 2 · 2 · x 9 = 3 · 3 There is no GCF and cannot be factored.

74. Factor Linear Expressions Factor the expression. 14x – 16y

75. Factor Linear Expressions Factor the expression. Method 1 14x – 16y 14x = 2 · 7 · x 16y = 2 · 2 · 2 · 2 · y The GCF is 2. 2(7x – 8y)

76. Factor Linear Expressions Factor the expression. Method 2 14x – 16y 2(7x – 8y)

77. Factor Linear Expressions Agenda Notes Homework – Homework Practice 7.5.8 due by the end of the period. Circle all answers and show all work with either method. Chapter 7.5 Test -Wednesday, May 20