1. Unit 4 Operations & Rules

2. 5x – 14 15x + 3 6x2 Warm up Combine Like Terms Exponent Rules
3) What is 2x  3x?
5x – 14
15x + 3
6x2

3. Degree
The exponent for a variable

4. Degree of the Polynomial
Highest (largest) exponent of the polynomial

5. Standard Form Terms are placed in descending order by the DEGREE
Write all answers in Standard Form!

6. Leading Coefficient
Once in standard form, it’s the 1st NUMBER in front of the variable (line leader)

7. # of Terms
Name by # of Terms
Monomial
Binomial
Trinomial
4+ Polynomial

8. Degree Name by degree 0 Constant 1 Linear 2 Quadratic 3 Cubic
(largest exponent)
Name by degree
Constant
1 Linear
2 Quadratic
3 Cubic

9. Linear Binomial -2 Special Names: Degree Name: # of Terms Name:
Leading Coefficient:
Binomial -2

10. Special Names:
Degree Name: # of Terms Name:
Cubic
Monomial

11. Quadratic Binomial 4 Special Names: Degree Name: # of Terms Name:
Leading Coefficient:
Binomial 4

12. Cubic Trinomial 1 Special Names: Degree Name: # of Terms Name:
Leading Coefficient:
Trinomial 1

13. Adding Polynomials

14. 1.
3x2 + x + 2

15. 2.
x2 + 2x – 2

16. Subtracting Polynomials

17. When SUBTRACTING polynomials Distribute the NEGATIVE

18. 3.
3a a – 8a2 + a
– 5a2 + 11a

19. 4.
3x2 + 2x – 4 – 2x2 – x + 1
x2 + x – 3

20. Multiplying Polynomials

21. 5.
-2x(x2 – 4x + 2)

22. (x + 3) (x – 3) 6.

23. (3x – 1)(2x – 4) 7.

24. 8. Find the area of the rectangle.

25. 9. Find the volume.

26. Warm up
Find an expression for the area of the following figure:

27. Challenge
Find an expression for the volume of cylinder:

28. Multiply:
Polynomial Ops Q8 of 20

29. Find the perimeter
Find the Perimeter:

30. Find an expression for the volume of cylinder:
Polynomial Ops Q11 of 20

31. Write an expression for the volume of the box:
Polynomial Ops Q14 of 20

32. Find the area of the label.
Polynomial Ops Q16 of 20

33. Skills Check

34. Square Roots and Simplifying Radicals

35. No number where the index is means it’s a square root (2)
Parts of a radical
No number where the index is means it’s a square root (2)

36. Radicals are in SIMPLEST FORM when..
1. No perfect square factors other than 1 are under the radical.
No fractions are under the radical.
No radicals are in the denominator.

37. You try! 1.

38. You try! 2.

39. You try! 3.

40. Variables Under Square Roots
Even Exponent –
ODD Exponent –
Take HALF out (nothing left under the radical)
Leave ONE under the radical and take HALF of the rest out

47. Nth Roots & Rational Exponents

48. No number where the root is means it’s a square root (2)
Parts of a radical
No number where the root is means it’s a square root (2)

49. Break down the radicand in to prime factors.
Simplifying Radicals
Break down the radicand in to prime factors.
Bring out groups by the number of the root.

50. Simplify

51. Simplify

52. Simplify

53. Simplify

54. Rewriting a Radical to have a Rational Exponent

55. Rewriting Radicals to Rational Exponents
Power is on top
Roots are in the ground

56. Rewriting Radicals to Rational Exponents
Power is on top
Roots are in the ground

57. Rewrite with a Rational Exponent

58. Rewrite with a Rational Exponent

59. Rewrite with a Rational Exponent

60. Rewrite with a Rational Exponent

61. Rewrite with a Rational Exponent

62. Rewriting Rational Exponents to Radicals

63. Rewrite with a Rational Exponent (don’t evaluate)

64. Rewrite with a Rational Exponent (don’t evaluate)

65. Rewrite with a Rational Exponent (don’t evaluate)

66. Warm up

67. Powers of i and Complex Operations

68. “I one, I one!!” Negatives in the middle.

69. Try these!

70. Add and Subtract Complex Numbers

71. Add/Subt Complex Numbers
Treat the i’s like variables
Combine the real parts then combine the imaginary parts
Simplify (no powers of i higher than 1 are allowed)
Write your answer in standard form a + bi

72. Simplify

73. Simplify

74. Simplify

75. Simplify

76. Simplify

77. Multiplying Complex Numbers

78. Multiplying Complex Numbers
Treat the i’s like variables
Simplify all Powers of i higher than 1
Combine like terms
Write your answer in standard form a + bi

79. Multiplying Complex Numbers

80. Multiplying Complex Numbers

81. Multiplying Complex Numbers

82. Dividing Complex Numbers

83. What is a Conjugate?

84. 17. Dividing – Multiply top & bottom by the Conjugate