5.6 Find each product.
63. 64. 65.
66. 67. 68.
69.Choose values for xand yto show that, in general, the following hold true.
(a) (b)
70.Write an explanation on how to raise a binomial to the third power. Give an example.
71.Refer to Exercise 69.Suppose that you happened to let and Would your
results be sufficient to illustrate the truth, in general, of the inequalities shown? If not,
what would you need to do as your next step in working the exercise?
x= 0 y=1.
1 x+y 22 Zx^2 +y^21 x+y 23 Zx^3 +y^3
15 a+ 6 b 215 a- 6 b 2 1 r+ 223 t 15 t- 322
1 a+ 422 12 r+ 5 t 22 16 m- 5216 m+ 52
72.Find a polynomial that represents, in
cubic centimeters, the volume of a cube
with one side having length
centimeters.
73.Find a polynomial that represents, in
cubic inches, the volume of a sphere with
1 x^2 + 22 radius inches. 1 x+ 12
(x^2 + 2) cm
A cube
(x^ + 1) in.
A sphere
5.7 Perform each division.
74. 75.
76.
77.Concept Check What polynomial, when multiplied by gives the product
78.Concept Check One of your friends in class simplified
as
WHAT WENT WRONG?Give the correct answer.
Perform each division.
81. 82.
83. 84.
85. 86.
87. 88.
4 x^5 - 8 x^4 - 3 x^3 + 22 x^2 - 15
4 x^2 - 3
6 y^4 - 15 y^3 + 14 y^2 - 5 y- 1
3 y^2 + 1
1000 x^6 + 1
10 x^2 + 1
y^3 - 8
y- 2
25 y^2 - 100
5 y+ 10
16 x^2 - 25
4 x+ 5
m^4 + 4 m^3 - 12 m- 5 m^2 + 6
m^2 - 3
x^4 - 5 x^2 + 3 x^3 - 3 x+ 4
x^2 - 1
10 a^3 + 9 a^2 - 14 a+ 9
5 a- 3
2 r^2 + 3 r- 14
r- 2
x^2 - 12 x.
6 x^2 - 12 x
6
12 m^3 n^2 + 18 m^6 n^3 - 24 m^2 n^2?
6 m^2 n,
1 - 10 m^4 n^2 + 5 m^3 n^2 + 6 m^2 n^42 , 15 m^2 n 2
6 y^4 - 12 y^2 + 18 y
6 y
354 CHAPTER 5 Exponents and Polynomials
In Exercises 72 and 73, if necessary, refer to the formulas on the inside covers.
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