1. 8-Chapter Notes
Algebra 1

2. Adding and Subtracting Polynomials
8-1 Notes Algebra 1
Adding and Subtracting Polynomials

3. 8.1 pg , 66-90(x3)

4. 6th degree, 7th degree, etc…
Polynomial
A monomial or the sum of monomials. (Each called a term) Some have special names (Monomial, Binomial and Trinomials) The degrees of the polynomials are:
Degree
Name
Constant 1
Linear 2
Quadratic 3
Cubic 4
Quartic 5
Quintic
6 or more
6th degree, 7th degree, etc…

5. Example 1: Identify polynomials
Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1.) 6𝑥−4 2.) 𝑥 2 +2𝑥𝑦−7 3.) 14𝑑+19𝑒 3 5𝑑 4 4.) 26𝑏 2

6. Example 1: Identify polynomials
Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial. 1.) 6𝑥−4 (Yes, Linear, Binomial) 2.) 𝑥 2 +2𝑥𝑦−7 (Yes, Quadratic, Trinomial) 3.) 14𝑑+19𝑒 3 5𝑑 4 (Not a polynomial) 4.) 26𝑏 2 (Yes, Quadratic, Monomial)

7. Standard form of a polynomial
Terms are listed in order from highest degree to lowest. When written in this form, the coefficient of the first term is called the leading coefficient.

8. Example 2: Standard of a Polynomial
Write each polynomial in standard form. Identify the leading coefficient. 1.) 9𝑥 2 + 3𝑥 6 −4𝑥 2.) 12+5𝑦+6𝑥𝑦+8𝑥𝑦 2

9. Example 2: Standard of a Polynomial
Write each polynomial in standard form. Identify the leading coefficient. 1.) 9𝑥 2 + 3𝑥 6 −4𝑥 2.) 12+5𝑦+6𝑥𝑦+8𝑥𝑦 2 3𝑥 6 + 9𝑥 2 −4𝑥; 3 8𝑥𝑦 2 +6𝑥𝑦+5𝑦+12; 8

10. Example 3: Add Polynomials
Find each Sum 1.) 7𝑦 2 +2𝑦−3 + 2−4𝑦+5𝑦 2 2.) 4𝑥 2 −2𝑥+7 + 3𝑥−7𝑥 2 −9

11. Example 3: Add Polynomials
Find each Sum 1.) 7𝑦 2 +2𝑦−3 + 2−4𝑦+5𝑦 2 12𝑦 2 −2𝑦−1 2.) 4𝑥 2 −2𝑥+7 + 3𝑥−7𝑥 2 −9 −3𝑥 2 +𝑥−2

12. Example 4: Subtracting Polynomials
Find each Difference 1.) 6𝑦 2 + 8𝑦 4 −5𝑦 − 9𝑦 4 −7𝑦+2𝑦 2 2.) 6𝑛 𝑛 3 +2𝑛 − 4𝑛−3+5𝑛 2

13. Example 4: Subtracting Polynomials
Find each Difference 1.) 6𝑦 2 + 8𝑦 4 −5𝑦 − 9𝑦 4 −7𝑦+2𝑦 2 −𝑦 4 + 4𝑦 2 +2𝑦 2.) 6𝑛 𝑛 3 +2𝑛 − 4𝑛−3+5𝑛 2 11𝑛 3 + 𝑛 2 −2𝑛+3

14. Example 5: Add and Subtract Polynomials
VIDEO GAMES The total amount of toy sales 𝑇 (in billions of dollars) consists of two groups: sales of video games V and sales of tradition toys 𝑅. In recent years, the sales of traditional toys and total sales could be represented by the following equations, where 𝑛 is the number of years since 𝑅= 0.46𝑛 3 − 1.9𝑛 2 +3𝑛+19 𝑇= 0.45𝑛 3 − 1.85𝑛 𝑛 ) Write an equation that represents the sales of video games 𝑉. 2.) Use the equation to predict the amount of video game sales in the year 2012.

15. Example 5: Add and Subtract Polynomials
VIDEO GAMES The total amount of toy sales 𝑇 (in billions of dollars) consists of two groups: sales of video games V and sales of tradition toys 𝑅. In recent years, the sales of traditional toys and total sales could be represented by the following equations, where 𝑛 is the number of years since 𝑅= 0.46𝑛 3 − 1.9𝑛 2 +3𝑛+19 𝑇= 0.45𝑛 3 − 1.85𝑛 𝑛 ) Write an equation that represents the sales of video games 𝑉. 𝑉=−0.01 𝑛 𝑛 𝑛 ) Use the equation to predict the amount of video game sales in the year 𝑏𝑖𝑙𝑙𝑖𝑜𝑛 𝑑𝑜𝑙𝑙𝑎𝑟𝑠

16. Multiplying a Polynomial by a Monomial
8-2 Notes For Algebra 1
Multiplying a Polynomial by a Monomial

17. 8-2 pg , 31-39o, 51-75(x3)

18. Multiplying a Polynomial by a Monomial
Use the Distributive Property

19. Example 1: Multiply a Polynomial by a Monomial
Find: 6𝑦 4𝑦 2 −9𝑦−7

20. Example 1: Multiply a Polynomial by a Monomial
Find: 6𝑦 4𝑦 2 −9𝑦−7 24𝑦 3 − 63𝑦 2 −42𝑦

21. Example 2: Simplify Expressions

22. Example 2: Simplify Expressions

23. Example 3: Write and Evaluate a Polynomial Expression
Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an additional $3 each, and regular rides are an additional $2. Wanda goes to the park and rides 15 rides, of which 𝑠 of those 15 are super rides. Find the cost in dollars if Wanda rode 9 super rides.

24. Example 3: Write and Evaluate a Polynomial Expression
Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an additional $3 each, and regular rides are an additional $2. Wanda goes to the park and rides 15 rides, of which 𝑠 of those 15 are super rides. Find the cost in dollars if Wanda rode 9 super rides. 49

25. Example 4: Equations with Polynomials on Both sides
Solve: 𝑏 12+𝑏 −7=2𝑏+𝑏 −4+𝑏

26. Example 4: Equations with Polynomials on Both sides
Solve: 𝑏 12+𝑏 −7=2𝑏+𝑏 −4+𝑏 𝑏= 1 2

27. Multiplying Polynomials
8-3 Notes for Algebra 1
Multiplying Polynomials

28. 8-3 pg , 25-41o, 51-66(x3)

29. Multiplying Binomials
You can multiply horizontally or vertically Multiply every term in the first group times each term in the last group.

30. Example 1: The Distributive Property
Find each Product 1.) 𝑦+8 𝑦−4 2.) 2𝑥+1 𝑥+6

31. Example 1: The Distributive Property
Find each Product 1.) 𝑦+8 𝑦−4 𝑦 2 +4𝑦−32 2.) 2𝑥+1 𝑥+6 2𝑥 2 +13𝑦+6

32. FOIL method

33. Example 2: FOIL method
Find each product. 1.) 𝑧−6 𝑧−12 2.) 5𝑥−4 2𝑥+8

34. Example 2: FOIL method
Find each product. 1.) 𝑧−6 𝑧−12 2.) 5𝑥−4 2𝑥+8 𝑧 2 −18𝑧+72 10𝑥 2 +32𝑥−32

35. Example 3: FOIL method
PATIO A patio in the shape of the triangle is being built in Linda’s backyard. The dimensions given are in feet. The area 𝐴 of the triangle is one half the height ℎ times the base 𝑏. Write an expression for the area of the patio.
𝑥−7
6𝑥+4

36. Example 3: FOIL method
PATIO A patio in the shape of the triangle is being built in Linda’s backyard. The dimensions given are in feet. The area 𝐴 of the triangle is one half the height ℎ times the base 𝑏. Write an expression for the area of the patio 𝑥 2 −19𝑥−14 𝑓𝑡 2
𝑥−7
6𝑥+4

37. Example 4: The Distributive Property
Find Each Product 1.) 3𝑎+4 𝑎 2 −12𝑎+1 2.) 2𝑏 2 +7𝑏+9 𝑏 2 +3𝑏−1

38. Example 4: The Distributive Property
Find Each Product 1.) 3𝑎+4 𝑎 2 −12𝑎+1 2.) 2𝑏 2 +7𝑏+9 𝑏 2 +3𝑏−1 3𝑎 3 −32 𝑎 2 −45𝑎+4 2𝑏 𝑏 𝑏 2 +20𝑏−9

39. 8-4 Notes for Algebra 1
Special Products

40. 8-4 pg , 22-44, 45-53o, 63-87(x3)

41. Square of Sums and Differences
𝑎+𝑏 2 = 𝑎+𝑏 𝑎+𝑏 = 𝑎 2 +2𝑎𝑏+ 𝑏 2 First term 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 Sign 2 𝑓𝑖𝑟𝑠𝑡 𝑙𝑎𝑠𝑡 + last term 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 𝑎−𝑏 2 = 𝑎−𝑏 𝑎−𝑏 = 𝑎 2 −2𝑎𝑏+ 𝑏 2

42. Example 1: Square of a Sum
Find. 7𝑧+2 2

43. Example 1: Square of a Sum
Find. 7𝑧 𝑧 2 +28𝑧+4

44. Example 2: Square of a Difference
Find. 3𝑐−4 2

45. Example 2: Square of a Difference
Find. 3𝑐−4 2 9𝑐 2 −24𝑐+16

46. Example 3: Square of a Difference
GEOMETRY Write an expression that represents the area of a square that has a side length of 3𝑥+12 units.

47. Example 3: Square of a Difference
GEOMETRY Write an expression that represents the area of a square that has a side length of 3𝑥+12 units. 9𝑥 2 +72𝑥+144 𝑢𝑛𝑖𝑡𝑠 2

48. Product of a Sum and a Difference
𝑎+𝑏 𝑎−𝑏 = 𝑎−𝑏 𝑎+𝑏 = 𝑎 2 − 𝑏 2 First term 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 − last term 𝑠𝑞𝑢𝑎𝑟𝑒𝑑

49. Example 4: Product of a Sum and Difference
Find. 9𝑑+4 9𝑑−4

50. Example 4: Product of a Sum and Difference
Find. 9𝑑+4 9𝑑−4 81𝑎 2 −16

51. Using the Distributive Property
8-5 Notes for Algebra 1
Using the Distributive Property

52. 8-5 pg , 63-84(x3)

53. Factoring
Breaking polynomials down into completely factored forms.

54. First Step of Factoring
Pull out the greatest common factor.
A polynomial is NOT completely factored unless there are NO common factors.

55. Example 1: Use the Distributive Property
Use the Distributive Property to factor each polynomial. 1.) 15𝑥+25 𝑥 2 2.) 12𝑥𝑦+24𝑥𝑦 2 − 30𝑥 2 𝑦 4

56. Example 1: Use the Distributive Property
Use the Distributive Property to factor each polynomial. 1.) 15𝑥+25 𝑥 2 2.) 12𝑥𝑦+24𝑥𝑦 2 − 30𝑥 2 𝑦 4 5x 3+5𝑥 6xy 2+4𝑦− 5𝑥𝑦 3

57. Factoring by Grouping
These conditions must exist to factor by grouping:
There are 4 or more terms
Terms have common factors that can be grouped together.
There are two common factors that are identical or additive inverse of each other.

58. Example 2: Factor by Grouping

59. Example 2: Factor by Grouping

60. Example 3: Factor by Grouping with Additive Inverses

61. Example 3: Factor by Grouping with Additive Inverses

62. Zero Product Property
If the product of 2 factors is zero, than at least one of the factors must be zero.

63. Example 4: Solve Equations
Solve each equation. Check your solutions. 1.) 𝑥−2 4𝑥−1 =0 2.) 4𝑦=12𝑦 2

64. Example 4: Solve Equations
Solve each equation. Check your solutions. 1.) 𝑥−2 4𝑥−1 =0 𝑥= 1 4 , 2 2.) 4𝑦=12𝑦 2 𝑥=0, 1 3

65. Example 5: Use Factoring
FOOTBALL A football is kicked into the air. The height of the football can be modeled by the equation ℎ=−16 𝑥 2 +16𝑥, where h is the height reached by the ball after 𝑥 seconds. Find the values of 𝑥 when ℎ=0.

66. Example 5: Use Factoring
FOOTBALL A football is kicked into the air. The height of the football can be modeled by the equation ℎ=−16 𝑥 2 +16𝑥, where h is the height reached by the ball after 𝑥 seconds. Find the values of 𝑥 when ℎ=0. 0 𝑠𝑒𝑐𝑜𝑛𝑑𝑠, 1 𝑠𝑒𝑐𝑜𝑛𝑑

67. Solving Quadratic Equtions with a leading coefficient of 1
8-6 Notes for Algebra 1
Solving Quadratic Equtions with a leading coefficient of 1

68. 8-6 pg , 33-36, 51-66(x3)

69. Factoring: 𝑥 2 +𝑏𝑥+𝑐
𝑥 2 +𝑏𝑥+𝑐 Find factors of 𝑐 that will add together to give you the middle term 𝑥 2 +𝑏𝑥−𝑐 Find factors of 𝑐 that will subtract from each other to give you the middle term.

70. Factoring using the Box Method 𝑥 2 +𝑏𝑥+𝑐
𝐹𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚×𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚 𝑥 𝑧 𝑐𝑥 2 = 𝑚 𝑝 List all factors of the product above, find the factors that will add them 𝑥 together to get the middle term 𝑏𝑥= 𝑚 + 𝑝 Place these factors in the other two 𝑤 squares and Pull the GCF up and left. 𝑥+𝑤 𝑥+𝑧
𝐹𝑖𝑟𝑠𝑡
𝑡𝑒𝑟𝑚 𝑚 𝑝
𝐿𝑎𝑠𝑡
𝑇𝑒𝑟𝑚

71. 𝑥 2 2𝑥 3𝑥 6 Example of Box method
𝑥 2 +5𝑥+6 6𝑥 2 Sum 𝑥 2 1𝑥∙6𝑥 7𝑥 −1𝑥∙−6𝑥 −7𝑥 𝑥 2𝑥∙3𝑥 5𝑥 −2𝑥∙−3𝑥 −5𝑥 3 𝑥+2 𝑥−3
𝑥 2 2𝑥 3𝑥 6

72. 𝑥 2 −1𝑥 6𝑥 −6 Example of Box method
𝑥 2 +5𝑥−6 − 6𝑥 2 Sum 𝑥 −1 −1𝑥∙6𝑥 5𝑥 1𝑥∙−6𝑥 −5𝑥 𝑥 −2𝑥∙3𝑥 𝑥 2𝑥∙−3𝑥 −𝑥 6 𝑥+6 𝑥−1
𝑥 2
−1𝑥 6𝑥 −6

73. Example 1: b and c are positive
Factor: 𝑥 2 +7𝑥=12

74. Example 1: b and c are positive
Factor: 𝑥 2 +7𝑥+12 𝑥+3 𝑥+4

75. Example 2: b is negative and c is Positive
Factor: 𝑥 2 −12𝑥+27

76. Example 2: b is negative and c is Positive
Factor: 𝑥 2 −12𝑥+27 𝑥−3 𝑥−9

77. Example 3 c is negative
Factor: 1.) 𝑥 2 +3𝑥−18 2.) 𝑥 2 −𝑥−20

78. Example 3 c is negative
Factor: 1.) 𝑥 2 +3𝑥−18 𝑥+6 𝑥−3 2.) 𝑥 2 −𝑥−20 𝑥−5 𝑥+4

79. Example 4: Solve an Equation by Factoring

80. Example 4: Solve an Equation by Factoring

81. Example 5: Solve a Problem by Factoring
ARCHITECTURE Marion wants to build a new art studio that has three times the area of her old studio by increasing the length and width of the old studio by the same amount. What should be the dimensions of the new studio? 𝑥 12 𝑓𝑡 10 𝑓𝑡 𝑥

82. Example 5: Solve a Problem by Factoring
ARCHITECTURE Marion wants to build a new art studio that has three times the area of her old studio by increasing the length and width of the old studio by the same amount. What should be the dimensions of the new studio? 𝑥 12 𝑓𝑡 The dimensions of the new studio 10 𝑓𝑡 should be 18 𝑓𝑡 by 20 𝑓𝑡. 𝑥

83. Solving Quadratic Equations with a leading coefficient other than 1
8-7 Notes for Algebra 1
Solving Quadratic Equations with a leading coefficient other than 1

84. 8-7 pg , 45-72(x3)

85. Factoring: 𝑎𝑥 2 +𝑏𝑥+𝑐
𝑎𝑥 2 +𝑏𝑥+𝑐 Find factors of 𝑎𝑐 that will add together to give you the middle term 𝑎𝑥 2 +𝑏𝑥−𝑐 Find factors of 𝑎𝑐 that will subtract from each other to give you the middle term.

86. Factoring using the Box Method 𝑥 2 +𝑏𝑥+𝑐
𝐹𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚×𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚 𝑥 𝑧 𝑐𝑥 2 = 𝑚 𝑝 List all factors of the product above, find the factors that will add them 𝑥 together to get the middle term 𝑏𝑥= 𝑚 + 𝑝 Place these factors in the other two 𝑤 squares and Pull the GCF up and left. 𝑥+𝑤 𝑥+𝑧
𝐹𝑖𝑟𝑠𝑡
𝑡𝑒𝑟𝑚 𝑚 𝑝
𝐿𝑎𝑠𝑡
𝑇𝑒𝑟𝑚

87. 2𝑥 2 4𝑥 3𝑥 6 Example of Box method
2 𝑥 2 +7𝑥+6 12𝑥 2 Sum 𝑥 2 1𝑥∙12𝑥 13𝑥 −1𝑥∙−12𝑥 −13𝑥 2𝑥 2𝑥∙6𝑥 8𝑥 −2𝑥∙−6𝑥 −8𝑥 3𝑥∙4𝑥 7𝑥 3 −3𝑥∙−4𝑥 −7𝑥 𝑥+2 𝑥−3
2𝑥 2 4𝑥 3𝑥 6

88. 2𝑥 2 −4𝑥 3𝑥 −6 Example of Box method
2 𝑥 2 −𝑥−6 −12𝑥 2 Sum 𝑥 −2 1𝑥∙−12𝑥 −11𝑥 −1𝑥∙12𝑥 11𝑥 2𝑥 2𝑥∙−6𝑥 −4𝑥 −2𝑥∙6𝑥 4𝑥 3𝑥∙−4𝑥 −𝑥 3 −3𝑥∙4𝑥 𝑥 𝑥−2 𝑥+3
2𝑥 2
−4𝑥 3𝑥 −6

89. Example 1: Factoring 𝑎𝑥 2 +𝑥+𝑐
Factor each Trinomial. 1.) 5𝑥 2 +27𝑥+10 2.) 4𝑥 2 +24𝑥+32

90. Example 1: Factoring 𝑎𝑥 2 +𝑥+𝑐
Factor each Trinomial. 1.) 5𝑥 2 +27𝑥+10 2.) 4𝑥 2 +24𝑥+32 5𝑥+2 𝑥+5 4 𝑥+2 𝑥+4

91. Example 2: Factor 𝑎𝑥 2 −𝑏𝑥+𝑐

92. Example 2: Factor 𝑎𝑥 2 −𝑏𝑥+𝑐

93. Prime Polynomial
A polynomial that cannot be written as a product of two polynomials with integral coefficients.

94. Example 3: Determine whether a polynomial is Prime
Factor. If the polynomial cannot be factored using integers, write prime. 3𝑥 2 +7𝑥−5

95. Example 3: Determine whether a polynomial is Prime
Factor. If the polynomial cannot be factored using integers, write prime. 3𝑥 2 +7𝑥−5 Prime

96. Example 4: Solve Equations by Factoring
MODEL ROCKETS Mr. Bird’s science class built a model rocket. They launched the rocket outside. It cleared the top of a 60-foot high pole and then landed in a nearby tree. If the launch pad was 2 feet above the ground, the initial velocity of the rocket was 64 feet per second, and the rocket landed 30 feet above the ground, how long was the rocket in flight? Use the equation ℎ=−16𝑡 2 +𝑣𝑡+ ℎ 0

97. Example 4: Solve Equations by Factoring
MODEL ROCKETS Mr. Bird’s science class built a model rocket. They launched the rocket outside. It cleared the top of a 60-foot high pole and then landed in a nearby tree. If the launch pad was 2 feet above the ground, the initial velocity of the rocket was 64 feet per second, and the rocket landed 30 feet above the ground, how long was the rocket in flight? Use the equation ℎ=−16𝑡 2 +𝑣𝑡+ ℎ 0 ≈3.5 𝑠𝑒𝑐𝑜𝑛𝑑𝑠

98. Differences of Squares
8-8 Notes for Algebra 1
2 − 2
Differences of Squares

99. 8-8 pg , 66-78(x3)

100. 8-8 Differences of perfect squares
𝑎 2 − 𝑏 2 𝑎−𝑏 𝑎+𝑏 1𝑠𝑡 𝑡𝑒𝑟𝑚 + 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚 1𝑠𝑡 𝑡𝑒𝑟𝑚 − 𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚

101. Example 1: Factor the Difference of perfect squares
Factor the polynomial 1.) 𝑚 2 −64 2.) 16𝑦 2 − 81𝑧 2 3.) 3𝑏 3 −27𝑏

102. Example 1: Factor the Difference of perfect squares
Factor the polynomial 1.) 𝑚 2 −64 2.) 16𝑦 2 − 81𝑧 2 3.) 3𝑏 3 −27𝑏 𝑚−8 𝑚+8 4𝑦−9𝑧 4𝑦+9𝑧 3𝑏 𝑏−3 𝑏+3

103. Example 2: Apply a Technique More than Once
Factor Each polynomial 1.) 𝑦 4 −625 2.) 256−𝑛 4

104. Example 2: Apply a Technique More than Once
Factor Each polynomial 1.) 𝑦 4 −625 2.) 256−𝑛 4 𝑦 𝑦+5 𝑦−5 16+𝑛 −𝑛

105. Example 3: Apply Different Techniques
Factor each polynomial 1.) 9𝑥 5 −36𝑥 2.) 6𝑥 𝑥 2 −24𝑥−120

106. Example 3: Apply Different Techniques
Factor each polynomial 1.) 9𝑥 5 −36𝑥 2.) 6𝑥 𝑥 2 −24𝑥−120 9x 𝑥 2 −2 𝑥 𝑥+2 𝑥−2 𝑥+5

107. Example 4: Solve an Equation by Factoring
In the equation 𝑦= 𝑞 2 − 4 25 , what is the value of 𝑞 when 𝑦=0?

108. Example 4: Solve an Equation by Factoring
In the equation 𝑦= 𝑞 2 − 4 25 , what is the value of 𝑞 when 𝑦=0? − 2 5

109. 8-9 Notes for Algebra 1
Perfect Squares

110. 8-9 pg , 63-75(x3)

111. Perfect Square Trinomials
The first term is a perfect square, the last term is a perfect square, and the middle term is found by doubling the product of the square root of the 1st term and the square root of the last term. 𝑎 2 +2𝑎𝑏 +𝑏 2 = 𝑎+𝑏 𝑎+𝑏 = 𝑎+𝑏 2 𝑎 2 −2𝑎𝑏 +𝑏 2 = 𝑎−𝑏 𝑎−𝑏 = 𝑎−𝑏 2

112. Example 1: Recognize and Factor Perfect Square Trinomials
Determine whether each trinomial is a perfect square trinomial. Write yes or no. If it is a perfect square, factor it. 1.) 25𝑥 2 −30𝑥+9 2.) 49𝑦 2 +42𝑦+36

113. Example 1: Recognize and Factor Perfect Square Trinomials
Determine whether each trinomial is a perfect square trinomial. Write yes or no. If it is a perfect square, factor it. 1.) 25𝑥 2 −30𝑥+9 2.) 49𝑦 2 +42𝑦+36 Yes, 5𝑥−3 2 No

114. Example 2: solve equations with repeated factors
Factor Completely. 1.) 6𝑥 2 −96 2.) 16𝑦 2 +8𝑦−15

115. Example 2: Factor Completely

116. Example 3: Solve Equations with Repeated factors

117. Example 3: Solve Equations with Repeated factors

118. Square root property
If 𝑥 2 =𝑛, then 𝑥=± 𝑛

119. Example 4: Use the Square Root Property
Solve each equation. Check the results. 1.) 𝑏−7 2 =36 2.) 𝑥+9 2 =8

120. Example 4: Use the Square Root Property
Solve each equation. Check the results. 1.) 𝑏−7 2 =36 𝑏=1, 13 2.) 𝑥+9 2 =8 𝑥=−9±2 2 𝑥≈−11.8, −6.2