Beginning Algebra, 11th Edition

87. 
    
    
    
    89. 
        
        
        
        91. 
            
        
        
        
        
    
    
    90. 
        
    
    
    
    

Section 5.7 (pages 346–348)

1. ; 2; 3. ; 2 (These may be reversed.);
   5.The first is a polynomial divided by a monomial, covered
   in Objective 1. This section does not cover dividing a monomial by a
   polynomial of several terms. 7. 9.


2. 
   
   
   
   13. 
       
       
       
       15. 
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   19. 
       
       
       
       21. 
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   25. 
       
       
       
       27. 
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   31. 
       
   
   
   
   


6. 
   
   
   
   35. 
       
       
       
       37. 
           
       
       
       
       
   
   
   36. 1423 40.
   
   
   
   


7. 42.They are similar in that
   the coefficients of powers of 10 are equal to the coefficients of the
   powers of x. They are different in that one is a constant while the other is a
   polynomial. They are equal if (the base of our decimal system).


8. 
   
   
   
   45. 
       
       
       
       47. 
           
           
           
           49. 
               
           
           
           
           
       
       
       
       
   
   
   
   


9. 
   
   
   
   53. 
       
       
       
       55. 
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    59. 
        
    
    
    
    


11. 
    
    
    
    63. 
        
        
        
        65. 
            
        
        
        
        
    
    
    64. 
        
        
        
        69. 
            
        
        
        
        
    
    
    
    


12. 
    
    
    
    73. 
        
        
        
        75. 
            
        
        
        
        
    
    
    
    


13. 
    
    
    
    79. 
        
        
        
        81. 
            
        
        
        
        
    
    
    80. 
        
        
        
        85. 
            
        
        
        
        
    
    
    
    


14. 89.1, 2, 3, 6, 9, 18 91.1, 2, 3, 4, 6, 8, 12,
    16, 24, 48

Chapter 5 Review Exercises (pages 352–355)

1. 
   
   
   
   2. 
      
      
      
      3. 
         
         
         
         4. 
            
            
            
            5. 
               
               
               
               6. 
                  
               
               
               
               
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   8. 
      
      
      
      9. 
         
         
         
         10. 
             
             
             
             11. 
                 
                 
                 
                 12. 13.The expression is a sumof powers of 7, not a product. 14. 2
                 
                 
                 
                 
             
             
             
             
         
         
         
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   16. 
       
       
       
       17. 
           
           
           
           18. 
               
               
               
               19. 
                   
                   
                   
                   20. 
                       
                       
                       
                       21. 
                           
                           
                           
                           22. 
                               
                           
                           
                           
                           
                       
                       
                       
                       
                   
                   
                   
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   24. 
       
       
       
       25. 
           
           
           
           26. 
               
               
               
               27. 
                   
                   
                   
                   28. 
                       
                       
                       
                       29. 
                           
                       
                       
                       
                       
                   
                   
                   
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   31. 32.24,000 33.78,300,000
       34.0.000000897 35. 800 36.4,000,000 37.0.025 38.0.000002
       39.0.0000000000016 40.4.2 1042 41.9.7 104 ;5* 103
   
   
   
   

2.8988* 1010 8.24* 10 -^8

(^172) r (^5) 4.8* 107
a^3 b^5
35
p^3
r^8
81
x^2 y^7
1
36
3
4
1
(^5881)
64

• 
  

  25
  1

  
  


• 
  

  1 - (^149)
  23 m^9 n^3
  (^6) p 6
  (^733) x (^6) y (^9) t (^422) x (^16) y (^4) z 16
  6
  5 p 56
  (^4) t 4
  411 1 - 5211 - 72 x^710 x^14195 x^51 - 427 y^7
  5 x^2 - 11 x+ 14
  (^1) x (^2) +x- 3 48 m (^2) + 96 m+ 24
  3
  +^4
  3 x- 3
  x^2 +
  8
  3 x-
  3
  2 a-^10 +
  77
  x 2 a+ 6
  (^3) + 3 x (^2) - x+ 5
  x^2 - 4 x+ 2 +
  9 x- 4
  x^2 + 3
  y^2 - y+ 1 a^2 + 1
  3 x^2 + 3 x- 1 +^1
  x- 1
  r^2 - 1 +^4
  r^2 - 1
  2 x+ 3 + -^1
  x+ 1
  2 p^3 - 6 p^2 + 7 p- 4 + x^2 + 3 x+ 3 2 x^2 -
  14
  3 p+ 1
  3 k^2 + 2 k- 2 +^6
  k- 2
  5 y^3 + 2 y- 3 + -^5
  y+ 1
  2 a- 14 +^744 x^2 - 7 x+ 3 4 k^3 - k+ 2
  2 a+ 3
  p- 4 + 6 m- 1
  44
  x+ 2 2 y- (^5) p+ 6
  x= 10
  13 1002 x^3 + 4 x^2 + 2 x+ 3
  2 xy^2 - x^4 y 11 1032 + 14 1022 + 12 1012 +
  6 x^4 y^2 - 4 xy+
  12
  x-
  6
  x^2

  
  

• 14
  x^3

• 10
  x^4


• 3 a+ 4 +
  5
  a


• m^2 + 3 m-
  4
  9 r m

(^3) - 12 r (^2) + 2 r+^26
3 -
2
3 r
4 x - 27 x (^3) + 10 x (^2) + 4
2
3
+x+^2
3 x
2 x+ 8 +^12
x
7 r^2 - 6 + 4 x^3 - 3 x^2 + 2 x - 9 x^2 + 5 x+ 1
1
r

• 3 p^2 - 2 +
  1
  p
  a^4 - a+
  2
  a
  4 t^4 - 2 t^2 + 2 t

30 x^3 - 10 x+ 5 4 m^3 - 2 m^2 + 1

10 x^2 + 8

10 x^2 + 8 5 x^2 + 4 5 x^2 + 4

3 k+ 3 5 t+ 3

• 24 k^3 + 36 k^2 - 6 k - 16 k^3 - 10 k^2 +
  m^2
  3

• 3 m- 2

Answers to Selected Exercises A-13

Section 5.5 (pages 333–334)

1. (a)B (b)D (c)A (d)C 3. 5. 7.


2. 
   
   
   
   11. 
       
       
       
       13. 
           
           
           
           15. 
               
           
           
           
           
       
       
       
       
   
   
   
   


3. 
   
   
   
   19. 
       
       
       
       21. 
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   25. 
       
   
   
   
   


5. 
   
   
   
   29. 
       
   
   
   
   


6. 
   
   
   
   33. 
       
   
   
   
   


7. 
   
   
   
   37. 
       
   
   
   38. 
       
   
   
   
   


8. 
   
   
   
   43. 
       
       
       
       45. 
           
       
       
       
       
   
   
   
   


9. 
   
   
   
   49. 
       
       
       
       51. 
           
       
       
       
       
   
   
   
   


10. 
    
    
    
    55. 
        
        
        
        57. 
            
        
        
        
        
    
    
    
    


11. 
    
    
    
    61. 
        
        
        
        63. 
            
        
        
        
        
    
    
    
    


12. 
    
    
    
    67. 
        
        
        
        69. (a)
            (b) 71. 73.
        
        
        
        
    
    
    
    


13. 
    
    
    
    77. 
        
        
        
        79. 
            
        
        
        
        
    
    
    
    


14. 
    
    
    
    83. 
        
    
    
    
    


15. 
    
    
    
    87. 
        
        
        
        89. 
            
        
        
        
        
    
    
    88. 
        
    
    
    
    


16. 
    
    
    
    95. 
        
    
    
    
    


17. 
    
    
    
    99. 
        
        
        
        101. 
             
             
             
             103. 
                  
             
             
             
             
        
        
        
        
    
    
    
    

Section 5.6 (pages 338–340)

1. (a) (b) 24 x (c) 9 (d) 3.


2. 
   
   
   
   7. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   


3. 
   
   
   
   13. 
       
   
   
   
   


4. 
   
   
   
   17. 
       
       
       
       19. 
           
       
       
       
       
   
   
   
   


5. (a) (b) 0 (c) (d) ; Because 0 is the
   identity element for addition, it is not necessary to write “ 0.”


6. 
   
   
   
   25. 
       
       
       
       27. 
           
           
           
           29. 
               
           
           
           
           
       
       
       
       
   
   
   
   


7. 
   
   
   
   33. 
       
       
       
       35. 
           
           
           
           37. 
               
           
           
           
           
       
       
       
       
   
   
   
   


8. 41.No. In general, equals ,
   which is not equivalent to 43.


9. 
   
   
   
   47. 
       
   
   
   
   


10. 
    
    
    
    51. 
        
    
    
    
    


11. 
    
    
    
    55. 
        
    
    
    56. 
        
        
        
        59. 
            
        
        
        
        
    
    
    
    


12. 
    
    
    
    62. 
        
        
        
        63. 2 ab 64. 65.
            66.They both represent the area of the entire large square. 67. 1225
        
        
        
        
    
    
    
    


13. 
    
    
    
    69. 1225 70.They are equal. 71. 9999
    
    
    
    

73.39,999 75. 77. 79.

81. 
    
    
    
    83. 
        
        
        
        85. 2 p+ 1 +
            4
            p
            px^2 + 4 px+ 4 p x^3 + 6 x^2 + 12 x+ 8
        
        
        
        
    
    
    
    

399 43 12 m^2 - 2 n^29 a^2 - 4

302 + 21302152 + 52

1 a+b 22 a^2 b^2 a^2 + 2 ab+b^2

6 x^2 + 2 x - 4 t^4 - 36 t^3 - 108 t^2 - 108 t x^4 - 2 x^2 y^2 +y^4

81 r^4 - 216 r^3 t+ 216 r^2 t^2 - 96 rt^3 + 16 t^42 x^4 + 6 x^3 +

8 a^3 + 12 a^2 + 6 a+ 1 256 x^4 - 256 x^3 + 96 x^2 - 16 x+ 1

t^3 - 9 t^2 + 27 t- 27 r^3 + 15 r^2 + 75 r+ 125

a^2 +b^2. x^3 + 3 x^2 + 3 x+ 1

25 q^3 - q 1 a+b 22 a^2 + 2 ab+b^2

100 x^2 - 9 y^24 x^4 - 25 169 - x^281 y^2 - 94

k^2 - 25 16 - 9 t^225 x^2 - 4 25 y^2 - 9 x^2

+

49 x^2 - 9 y^249 x^2 - 9 y^2

9 t^3 - 6 t^2 +t 48 t^3 + 24 t^2 + 3 t - 16 r^2 + 16 r- 4

16 a^2 + 40 ab+ 25 b^236 m^2 -^485 mn+ 2516 n^2

r^2 - 6 r+ 9 x^2 + 4 xy+ 4 y^225 p^2 + 20 pq+ 4 q^2

16 x^216 x^2 + 24 x+ 9 m^2 + 4 m+ 4

px^2 - 9 9 m^24 r^216 x^4

36 p^5 + 15 p^4 - 24 x^8 - 28 x^7 + 32 x^6 + 20 x^514 x+ 49

216 r^3 s+ 216 r^2 s^2 - 96 rs^3 + 16 s^46 p^8 + 15 p^7 + 12 p^6 +

• 9 a^3 + 33 a^2 + 12 a 56 m^2 - 14 m- 21 81 r^4 -

m^3 - 15 m^2 + 75 m- 125 8 a^3 + 12 a^2 + 6 a+ 1

a^2 - 16 4 p^2 - 20 p+ 25 25 k^2 + 30 kq+ 9 q^2

8 y+ 16 6 p^2 - 25 pq- 1225 q^2 x^2 + 14 x+ 49

6 y^5 - 21 y^4 - 45 y^3 - 200 r^7 + 32 r^33 y^2 + 10 y+ 7

3 t^2 + 5 st- 12 s^28 xy- 4 x+ 6 y- 3 15 x^2 +xy- 6 y^2

10 a^2 + 37 a+ 7 12 + 8 m- 15 m^220 - 7 x- 3 x^2

12 x^2 + 10 x- 12 81 - t^29 x^2 - 12 x+ 4

m^2 + 12 m+ 35 n^2 + 3 n- 4 x^2 - 25

20 x^2 + 7 x+ 5 3 x^5 + 18 x^4 - 2 x^3 - 8 x^2 + 24 x

6 x^6 - 3 x^5 - 4 x^4 + 4 x^3 - 5 x^2 + 8 x- 3 5 x^4 - 13 x^3 +

72 y^3 - 70 y^2 + 21 y- 2 20 m^4 - m^3 - 8 m^2 - 17 m- 15

21 m^5 n^2 + 14 m^4 n^3 - 7 m^3 n^512 x^3 + 26 x^2 + 10 x+ 1

28 r^5 - 32 r^4 + 36 r^36 a^4 - 12 a^3 b+ 15 a^2 b^2

• 6 p^4 + 12 p^3 - 16 z^2 - 24 z^3 - 24 z^46 y^3 + 4 y^4 + 10 y^7


• 18 m^3 n^29 y^10 - 8 x^106 m^2 + 4 m

15 y^1130 a^915 pq^2

95.4, 1, 0, 1, 4

x

y

9

–6–3 0

4

y = (x + 3)^2

97.63; If a dog is 9 in dog years, then it is 63 in

human years. 98.about 26 99.2.5; 130

100.6; $27 101. 103.

105.- 10 a^2 b 107.-m^7

5 x+ 20 8 a+ 24 b