Beginning Algebra, 11th Edition

(Marvins-Underground-K-12) #1

Summary Exercises on Factoring^391


61. 62.

63. 64.

65. 66.

67. 68.

69. 70.

71. 72.

73. 74.

75. 76.

77. 78.

79. 80.

81. 82.

83. 84.

85. 86.

87. 88.


  1. 8 a^2 + 23 ab- 3 b^2 90.a^4 - 625


10 y^2 - 7 yz- 6 z^2 m^2 - 4 m+ 4

2 x^3 + 128 8 a^3 - 27

8 k^2 - 2 kh- 3 h^22 a^2 - 7 a- 30

64 m^2 - 80 mn+ 25 n^272 y^3 z^2 + 12 y^2 - 24 y^4 z^2

a^3 - b^3 + 2 a- 2 b 16 k^2 - 48 k+ 36

6 a^2 + 10 a- 4 36 y^6 - 42 y^5 - 120 y^4

20 + 5 m+ 12 n+ 3 mn 4 - 2 q- 6 p+ 3 pq

32 z^3 + 56 z^2 - 16 z 10 m^2 + 25 m- 60

x^2 - xy+y^24 y^2 - 25

108 m^2 - 36 m+ 3 100 a^2 - 81 y^2

16 z^2 - 8 z+ 1 125 m^4 - 400 m^3 n+ 195 m^2 n^2

6 + 3 m+ 2 p+mp 2 m^2 + 7 mn- 15 n^2

1000 p^3 + 27 64 r^3 - 343

3 k^3 - 12 k^2 - 15 k y^2 - 4 yk- 12 k^2

EXERCISES 91–98

FOR INDIVIDUAL OR GROUP WORK
A binomial may be both a difference of squares and a difference of cubes. One
example of such a binomial is. With the techniques of Section 6.4,one
factoring method will give the completely factored form, while the other will not. Wo r k
Exercises 91–98 in orderto determine the method to use if you have to make such a
decision.
91.Factor as the difference of squares.
92.The factored form obtained in Exercise 91consists of a difference of cubes
multiplied by a sum of cubes. Factor each binomial further.
93.Now start over and factor as the difference of cubes.
94.The factored form obtained in Exercise 93 consists of a binomial that is a
difference of squares and a trinomial. Factor the binomial further.
95.Compare your results in Exercises 92 and 94.Which one of these is factored
completely?
96.Verify that the trinomial in the factored form in Exercise 94is the product of the
two trinomials in the factored form in Exercise 92.
97.Use the results of Exercises 91–96 to complete the following statement: In
general, if I must choose between factoring first with the method for the
difference of squares or the method for the difference of cubes, I should choose
the method to eventually obtain the completely factored form.
98.Find the completelyfactored form of by using the knowledge you
gained in Exercises 91–97.

x^6 - 729

x^6 - 1

x^6 - 1

x^6 - 1

RELATING CONCEPTS

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