Beginning Algebra, 11th Edition

SECTION 5.7 Dividing Polynomials^347

28.Concept Check If is divided by what is the sum of the

coefficients of the third- and second-degree terms in the quotient?

Perform each division. See Examples 1–4.

29. 
    
    
    
    30. 
        
    
    
    
    

31. 32.

33. 34.

35.

36.

37.

38. 1200 a^5 b^6 - 160 a^4 b^7 - 120 a^3 b^9 + 40 a^2 b^22 , 140 a^2 b 2

1120 x^5 y^4 - 80 x^2 y^3 + 40 x^2 y^4 - 20 x^5 y^32 , 120 xy^22

1120 x^12 - 84 x^9 + 60 x^8 - 36 x^72 , 112 x^92

1120 x^11 - 60 x^10 + 140 x^9 - 100 x^82 , 110 x^122

120 a^4 - 15 a^5 + 25 a^32 , 15 a^42136 y^2 - 12 y^3 + 20 y 2 , 14 y^22

6 r^5 - 8 r^4 + 10 r^2

• 2 r^4

2 m^5 - 6 m^4 + 8 m^2

• 2 m^3
  
  
  • 8 k^4 + 12 k^3 + 2 k^2 - 7 k+ 3
    
    
    • 2 k
    
    
    
    
  
  
  
  


• 27 r^4 + 36 r^3 - 6 r^2 - 26 r+ 2


• 3 r


• 60 x^5 - 30 x^4 + 20 x^33 x^2 ,

EXERCISES 39– 42

FOR INDIVIDUAL OR GROUP WORK

Our system of numeration is called a decimal system. In a whole number such as 2846,

each digit is understood to represent the number of powers of 10 for its place value. The

2 represents two thousands ,the 8 represents eight hundreds ,the

4 represents four tens ,and the 6 represents six ones (or units).

Expanded form

Keeping this information in mind, work Exercises 39– 42 in order.

39.Divide 2846 by 2, using paper-and-pencil methods:.

40.Write your answer from Exercise 39in expanded form.

41.Divide the polynomial by 2.

42.How are your answers in Exercises 40 and 41similar? Different? For what

value of xdoes the answer in Exercise 41equal the answer in Exercise 40?

2 x^3 + 8 x^2 + 4 x+ 6

2  2846

2846 = 12 1032 + 18 1022 + 14 1012 + 16 1002

14 1012 16 1002

12 1032 18 1022

RELATING CONCEPTS

Perform each division using the “long division” process. See Examples 5 and 6.

43. 
    
    
    
    44. 
        
        
        
        45. 
            
        
        
        
        
    
    
    
    

46. 47. 48.

49. 50. 51.

52. 53. 54.

55. 56.

57. 58.

59. 60.

61. 62.

6 r^4 - 11 r^3 - r^2 + 16 r- 8

2 r- 3

6 p^4 - 16 p^3 + 15 p^2 - 5 p+ 10

3 p+ 1

5 z^3 - z^2 + 10 z+ 2

z+ 2

3 k^3 - 4 k^2 - 6 k+ 10

k- 2

2 r^3 - 5 r^2 - 6 r+ 15

r- 3

5 y^4 + 5 y^3 + 2 y^2 - y- 8

y+ 1

27 r^4 - 36 r^3 - 6 r^2 + 26 r- 24

3 r- 4

8 k^4 - 12 k^3 - 2 k^2 + 7 k- 6

2 k- 3

12 t^3 - 11 t^2 + 9 t+ 18

4 t+ 3

8 x^3 - 10 x^2 - x+ 3

2 x+ 1

9 w^2 + 6 w+ 10

3 w- 2

4 a^2 - 22 a+ 32

2 a+ 3

12 y^2 + 20 y+ 7

2 y+ 1

12 m^2 - 20 m+ 3

2 m- 3

x^2 + 11 x+ 16

x+ 8

p^2 + 2 p+ 20

p+ 6

2 y^2 + 9 y+ 7

y+ 1

2 y^2 + 9 y- 35

y+ 7

m^2 - 2 m- 24

m- 6

x^2 - x- 6

x- 3