- ;;; 44. ;
degree 2; monomial 45. ; degree 3; none of these
46.already in descending powers; degree 5; none of these
- ;;; 44. ;
- ; degree 5; trinomial 48. ;
degree 4; trinomial 49. 50.
- 53.1, 4, 5, 4, 1 54.10, 1, , 1, 10
- (a)Answers will vary. For example, let
and because (b)Answers
will vary. For example, let and
because 70.To find the third power of a binomial, such as
first square the binomial and then multiply that result by the
binomial.
71.In both cases, and lead to
1 on each side of the inequality. This would not be sufficient to show that,
in general,the inequality is true. It would be necessary to choose other
values of xand y. 72. 73. , or
- (a)Answers will vary. For example, let
- 78.The friend
wrote the second term of the quotient as rather than Here is
the correct method. 79.
- 2
- (a)
(b) 108. (a) (b)
Chapter 5 Test (pages 355–356)
[5.1, 5.2]1. 2. 2 3. 4. 5. 6.
- (a)positive (b)positive (c)negative (d)positive (e)zero
(f )negative [5.3]8. (a) (b)0.0000036 (c)0.00019 - (a) 1 103 ; 5.89 1012 (b)5.89* 1015 mi
4.5* 10106251 127 9 x^3 y^585 x^2 y^62 x^2 +x- 6 20 x^4 + 8 x^225 x^8 + 20 x^6 + 4 x^46 x- 2
149 - 28 k+ 4 k x (^4) y 12
(^802)
x- 3
10 p^2 - 3 p- 5 3 x^2 + 9 x+ 25 +
5
2
- 4
5 xy
- 3 x
2 y^2
- y^2 - 4 y+ 4 10 r^2 + 21 r- 10 y^2 + 5 y+ 1
6 k^3 - 21 k- 6 r^134 r^2 + 20 rs+ 25 s^2
2
3 m^3p- 3 +^5
2 p1
8121
144 a 16(^62) - 1
(^3) r (^6) p 3
53
x^3 - 2 x^2 + 4 +
- 3
2 y 4 x (^2) - 3
(^2) - 5 y+ 4 + -^5
3 y^2 + 1
4 x- 5 5 y- 10 y^2 + 2 y+ 4 100 x^4 - 10 x^2 + 1
2 a^2 + 3 a- 1 +^6 x^2 + 3 x- 4 m^2 + 4 m- 2
5 a- 3
6 x x (^2) - 2 x 2 r+ 7
(^2) - 12 x
6
=^6 x
2
6
-^12 x
6
=
- 12 x - 2 x.
- 2 m^2 n+mn+ 2 mn+ 3 m^4 n^2 - 4 n
6 n^3
5
y^3 - 2 y+ 3- 5 y^2
3
4
4 px^2 + 4 px+ 3 p
4
3 px^3 +
4
x^6 + 6 x^4 + 12 x^2 + 8 3 p 1 x+ 123a^3 + 3 a^2 b+ 3 ab^2 +b^3 x= 0 y= 1
1 a+b 23 = 1 a+b 221 a+b 2 = 1 a^2 + 2 ab+b^221 a+b 2 =1 a+b 23 ,
27 Z9.x= 1 y=2. 11 + 223 Z 13 + 23 ,x= 1 y=2. 11 + 222 Z 12 + 22 , 9 Z5.
25 t^3 - 30 t^2 + 9 t36 m^2 - 25 25 a^2 - 36 b^2 r^3 + 6 r^2 + 12 r+ 8s^3 - 3 s^2 + 3 s- 1 a^2 + 8 a+ 16 4 r^2 + 20 rt+ 25 t^26 k^2 - 9 k- 6 2 a^2 + 5 ab- 3 b^212 k^2 - 32 kq- 35 q^25 p^5 - 2 p^4 - 3 p^3 + 25 p^2 + 15 p m^2 - 7 m- 18a^3 - 2 a^2 - 7 a+ 2 6 r^3 + 8 r^2 - 17 r+ 6xy–2y = 3x^2 – 2- 2
xy025y = –x^2 + 5y^2 - 10 y+ 9 - 13 k^4 - 15 k^2 + 18 k13 x^3 y^2 - 5 xy^5 + 21 x^2 a^3 + 4 a^2- 8 y^5 - 7 y^4 + 9 y 7 r^4 - 4 r^3 + 1
p^3 - p^2 + 4 p+ 21 * 10100 1 * 1032 * 1035 * 1041 * 105 22 m^2 [5.4]10. ; 2; binomial 11. 4; trinomial
12.xy
04–4–2 2
y = 2x^2 – 44, -2, -4, -2, 4- 7 x^2 + 8 x 4 n^4 + 13 n^3 - 10 n^2 ;
A-14 Answers to Selected Exercises
[5.1, 5.2]29. 30. 1 31. [5.3]32.about 10,800,000 km
[5.4]33.xy–4 04y = (x + 4)^22 b
a^105
4
34.
[5.5]35.
[5.7]36.y^2 - 2 y+ 663 x^2 + 57 x+ 1211 x^3 - 14 x^2 - x+ 14[5.6]19. 20.
[5.5]21. [5.6]22.
[5.7]23. 24. 25.26.Chapters 1–5 Cumulative Review Exercises
(pages 357–358)
[1.1]1. 2. 5 3. [1.6]4.$1836 5.1, 3, 5, 9, 15, 45
- [1.5]8. [1.7]9.associative property
10.distributive property [1.8]11.
[2.1–2.3]12. 13. [2.5]14. [2.6]15.
[2.1–2.3]16. 17. 18.
[2.4]19.exertion: 9443 calories; regulating body temperature:
1757 calories [2.8]20.11 ft and 22 ft 21. 22.
[3.2]23.
- [1.5]8. [1.7]9.associative property
xy260y = –3x + 6A-q, -^145 B^3 - 4, 2^25 - 126 5206 5 all real numbers 6r=d 5 - 56
t
E^134 F^0- 10 x^2 + 21 x- 29
- 8 12 - 4
(^743114) yd 3
3 x^2 + 6 x+ 11 +^26
x- 2
4 y^2 - 3 y+ 2 + - 3 xy^2 + 2 x^3 y^2 + 4 y^2 x- 2
5
y
2 r^3 +r^2 - 16 r+ 15 12 x+36; 9 x^2 + 54 x+ 81
25 x^2 - 20 xy+ 4 y^2100 v^2 - 9 w^2
13.
14.
15.
[5.5]16.
17.t^2 - 5 t- 24 18. 8 x^2 + 2 xy- 3 y^2
- 27 x^5 + 18 x^4 - 6 x^3 + 3 x^2
- 12 t^2 + 5 t+ 8
- 21 a^3 b^2 + 7 ab^5 - 5 a^2 b^2
- 2 y^2 - 9 y+ 17
[3.3, 3.4]24. (a) 1 (b)
[3.5]25.no [3.6]26.
[4.2]27.
[4.3]28. 51 4, - 52651 - 3, - 126- 1
y=x+ 6FACTORING AND APPLICATIONSSection 6.1 (pages 365–367)- 4 3. 6 5. 1 7. 8 9. 11. 13. 15.factored
17.not factored 19. 21. 23. 25.
- 31.First, verify that you have factored com-
pletely. Then multiply the factors. The product should be the original
polynomial. 33. 35. 37.
- 31.First, verify that you have factored com-
- 45.in factored form 47. 49.
- 61.not in factored form; 63.in factored form
65.not in factored form 67.The quantities in parentheses are not the
same, so there is no common factor of the two terms
and. 71 y- 42 69. 1 p+ 421 p+q 2 71. 1 a- 221 a+b 2
- 61.not in factored form; 63.in factored form
18 x^21 y+ 4217 t+ 4218 +x 21 x+ 221 c-d 2 1 m+ 2 n 21 m+n 2 1 p- 421 q^2 + 129 p^3 q 14 p^3 + 5 p^2 q^3 + 9 q 2 a^31 a^2 + 2 b^2 - 3 a^2 b^2 + 4 ab^328 mn^311 + 3 m 2 13 y^21 y^6 + 2 y^2 - 328 z^212 z^2 + 32 6 x^212 x+ 12 5 y^6113 y^4 + 72x 1 x- 42 3 t 12 t+ 52 9 m 13 m^2 - 12a- 2 2 + 3 xy3 m^22 z^42 mn^4 y+ 210 x^3 xy^26 m^3 n^26http://www.ebook777.com
http://www.ebook777.com