1. Section 5.1
Polynomials Addition And Subtraction

2. OBJECTIVES A
Classify polynomials.

3. OBJECTIVES Find the degree of a polynomial and write descending order.

4. OBJECTIVES C
Evaluate a polynomial.

5. OBJECTIVES D
Add or subtract polynomials.

6. OBJECTIVES E
Solve applications involving sums or differences of polynomials.

7. Degree of a Polynomial in One Variable
DEFINITION
Degree of a Polynomial in One Variable
The degree of a polynomial in one variable is the greatest exponent of that variable.

8. Degree of a Polynomial in Several Variables
DEFINITION
Degree of a Polynomial in Several Variables
The greatest sum of the exponents of the variables in any one term of the polynomial.

9. Properties for Adding Polynomials
RULES
Properties for Adding Polynomials

10. Properties for Adding Polynomials
RULES
Properties for Adding Polynomials

11. Properties for Adding Polynomials
RULES
Properties for Adding Polynomials

12. Subtracting Polynomials
RULES
Subtracting Polynomials

13. Chapter 5
Section 5.1A,B
Exercise #1

14. Classify as a monomial, binomial, or trinomial and
give the degree.
Binomial.
Degree is determined by comparing
Degree 8

15. Chapter 5
Section 5.1D
Exercise #5

16. METHOD 1

17. METHOD 2

18. Chapter 5
Section 5.1D
Exercise #6

19. METHOD 1

20. METHOD 1

21. METHOD 1

22. METHOD 2

23. Section 5.2
Multiplication of Polynomials

24. OBJECTIVES A
Multiply a monomial by a polynomial.

25. OBJECTIVES B
Multiply two polynomials.

26. OBJECTIVES C
Use the FOIL method to multiply two binomials.

27. OBJECTIVES D
Square a binomial sum or difference.

28. OBJECTIVES E
Find the product of the sum and the difference of two terms.

29. OBJECTIVES F
Use the ideas discussed to solve applications.

30. Multiplication of Polynomials
RULES
Multiplication of Polynomials

31. USING FOIL
To Multiply Two Binomials
(x + a)(x + b)

32. RULE
To Square a Binomial Sum

33. RULE
To Square a Binomial Difference

34. Sum and Difference of Same Two Monomials
PROCEDURE
Sum and Difference of Same Two Monomials

35. Chapter 5
Section 5.2B,C
Exercise #8a

36. METHOD 1

37. METHOD 2

38. Chapter 5
Section 5.2D
Exercise #9b

40. Chapter 5
Section 5.2E
Exercise #10

41. Product of Sum and Difference of Same Two Monomials

42. Section 5.3
The Greatest Common Factor and Factoring by Grouping

43. OBJECTIVES A
Factor out the greatest common factor in a polynomial.

44. OBJECTIVES B
Factor a polynomial with four terms by grouping.

45. GREATEST COMMON FACTOR
is the Greatest Common monomial Factor (GCF) of a polynomial in x if:
1. a is the greatest integer that divides each coefficient.

46. GREATEST COMMON FACTOR
is the Greatest Common monomial Factor (GCF) of a polynomial in x if:
2. n is the smallest exponent of x in all the terms.

47. PROCEDURE Factoring by Grouping Group terms with common
factors using the
associative property.

48. PROCEDURE
Factoring by Grouping
Factor each resulting
binomial.

49. PROCEDURE Factoring by Grouping Factor out the binomial
using the GCF, by the
distributive property.

50. Chapter 5
Section 5.3B
Exercise #12

52. Section 5.4
Factoring Trinomials

53. OBJECTIVES A
Factor a trinomial of the form

54. OBJECTIVES B
Factor a trinomial of the form using trial and error.

55. OBJECTIVES C
Factor a trinomial of the form using the ac test.

56. PROCEDURE
Factoring Trinomials

57. RULE The ac Test is factorable only if there are two integers
whose product is ac and
sum is b.

58. Chapter 5
Section 5.4A,B,C
Exercise #13b

59. The ac Method Find factors of ac (–20) whose sum is (1) and replace the middle term (xy).

60. Section 5.5
Special Factoring

61. OBJECTIVES A
Factor a perfect square trinomial.

62. OBJECTIVES B
Factor the difference of two squares.

63. OBJECTIVES C
Factor the sum or difference of two cubes.

64. Factoring Perfect Square Trinomials
PROCEDURE
Factoring Perfect Square Trinomials

65. Factoring the Difference of
PROCEDURE
Factoring the Difference of
Two Squares

66. Factoring the Sum and Difference of Two Cubes
PROCEDURE
Factoring the Sum and Difference of Two Cubes

67. Chapter 5
Section 5.5A
Exercise #15a

69. Chapter 5
Section 5.5
Exercise #16

70. Difference of Two Squares

71. Chapter 5
Section 5.5B
Exercise #17

72. Perfect Square Trinomial
Difference of Two Squares

73. Chapter 5
Section 5.5c
Exercise #18a

74. Sum of Two Cubes

75. Section 5.6
General Methods of Factoring

76. OBJECTIVES Factor a polynomial using the procedure given in the text.

77. PROCEDURE A General Factoring Strategy Factor out the GCF, if
there is one.
Look at the number of terms
in the given polynomial.

78. PROCEDURE A General Factoring Strategy
If there are two terms, look for:

79. PROCEDURE A General Factoring Strategy
If there are two terms, look for:

80. PROCEDURE A General Factoring Strategy
If there are two terms, look for:

81. PROCEDURE A General Factoring Strategy
If there are two terms, look for:
The sum of two squares,
is not factorable.

82. PROCEDURE A General Factoring Strategy
If there are three terms, look for:
Perfect square trinomial

83. PROCEDURE A General Factoring Strategy
If there are three terms, look for:
Trinomials of the form

84. PROCEDURE A General Factoring Strategy Use the ac method or
trial and error.

85. PROCEDURE A General Factoring Strategy If there are four terms:
Factor by grouping.

86. PROCEDURE A General Factoring Strategy Check the result by
multiplying the factors.

87. Chapter 5
Section 5.6A
Exercise #20b

88. Perfect Square Trinomial

89. Chapter 5
Section 5.6A
Exercise #21

90. The ac Method Find factors of ac (–12) whose sum is (–11) and replace the middle term (–11xy).

91. The ac Method Find factors of ac (–12) whose sum is (–11) and replace the middle term (–11xy).

92. Chapter 5
Section 5.6A
Exercise #22

93. Difference of Two Squares

94. Section 5.7
Solving Equations by Factoring: Applications

95. OBJECTIVES A
Solve equations by factoring.

96. OBJECTIVES B
Use Pythagorean theorem to find the length of one side of a right triangle when the lengths of the other two sides are given.

97. OBJECTIVES C
Solve applications involving quadratic equations.

98. PROCEDURE Set equation equal to 0. O Factor Completely. F
Set each linear Factor
equal to 0 and solve each. F

99. DEFINITION
Pythagorean Theorem c a b

100. Chapter 5
Section 5.7A
Exercise #23b

101. O F F or or