Intermediate Algebra (11th edition)

282 CHAPTER 5 Exponents, Polynomials, and Polynomial Functions

Complete solution available
on the Video Resources on DVD

5.2 EXERCISES

Give the numerical coefficient and the degree of each term. See Objective 1.

1. 7 z 2. 3 r 3. 4. 5. 6.


2. 
   
   
   
   8. 
      
      
      
      9. 8 10. 2 11. 12.
      
      
      
      
   
   
   
   

Write each polynomial in descending powers of the variable. Then give the leading term and

the leading coefficient. See Example 1.

Identify each polynomial as a monomial, binomial, trinomial,or none of these.Also, give the

degree. See Example 2.

19. 25 20. 15 21. 22.


20. 
    
    
    
    24. 
        
        
        
        25. 
            
            
            
            26. 
                
            
            
            
            
        
        
        
        
    
    
    
    


21. 
    
    
    
    28. 
        
    
    
    
    


22. 
    
    
    
    30. 31.Concept Check Which one of the following is a trinomial in descending powers, having
        degree 6?
        A. B.
        C. D.
        32.Concept Check Give an example of a polynomial of four terms in the variable x, having
        degree 5, written in descending powers, and lacking a fourth-degree term.
    
    
    
    

Combine like terms. See Example 3.

33. 
    
    
    
    34. 
        
        
        
        35. 
            
        
        
        
        
    
    
    
    


34. 
    
    
    
    37. 
        
        
        
        38. 
            
        
        
        
        
    
    
    
    


35. 
    
    
    
    40. 
        
        
        
        41. 
            
        
        
        
        
    
    
    
    


36. 
    
    
    
    43. 
        
        
        
        44. 
            
        
        
        
        
    
    
    
    


37. 
    
    
    
    46. 
        
    
    
    
    


38. 
    
    
    
    48. 
        
    
    
    
    


39. 
    
    
    
    50. 
        
    
    
    
    


40. 6 + 3 p- 12 p+ 12 - 12 p+ 92 52. 4 x- 8 - 1 - 1 +x 2 - 111 x+ 52

4 - 12 + 3 m 2 + 6 m+ 9 8 a- 13 a+ 42 - 15 a- 32

3 ab^2 + 7 a^2 b- 5 ab^2 + 13 a^2 b 6 m^2 n- 8 mn^2 + 3 mn^2 - 7 m^2 n

n^4 - 2 n^3 +n^2 - 3 n^4 +n^32 q^3 + 3 q^2 - 4 q-q^3 + 5 q^2

8 p- 9 q- 3 p+q 2 k+ 3 k^2 + 5 k^2 - 7 4 x^2 + 2 x- 6 x^2 - 6

m^4 - 3 m^2 +m 5 a^5 + 2 a^4 - 9 a^35 t+ 4 s- 6 t+ 9 s

3 p^4 + 5 p^4 - 2 p^4 x+x+x+x+x z-z-z+z

5 z^4 + 3 z^48 r^5 - 2 r^5 - m^3 + 2 m^3 + 6 m^3

2 x+ 4 x^2 - x^64 x^6 - 6 x^4 + 9 x^2 - 8

5 x^6 - 4 x^5 + 12 6 x^5 - x^6 + 4

• 6 p^4 q- 3 p^3 q^2 + 2 pq^3 - q^48 s^3 t- 4 s^2 t^2 + 2 st^3 + 9


• 5 m^3 + 6 m- 9 m^24 z^2 - 11 z+ 2


• 7 y^6 + 11 y^812 k^2 - 9 k^5 - mn^5 - a^3 b

7 m- 22 6 x+ 15

3 y^2 +y^4 - 2 y^310 - m^3 - 3 m^44 - x- 8 x^2

2 x^3 +x- 3 x^2 + 4 q^2 + 3 q^4 - 2 q+ 1 4 p^3 - 8 p^5 +p^7

• x^3 - y^9

m

4

t

6

• 15 p^2 - 27 k^3 x^4 y^6

Add or subtract as indicated. See Examples 4 and 5.

53. 
    
    
    
    54. 
        
    
    
    
    


54. 
    
    
    
    56. 
        
    
    
    
    


55. 
    
    
    
    58. 
        
    
    
    
    


56. 
    
    
    
    60. 
        
    
    
    
    


57. 
    
    
    
    62. 
        
    
    
    
    


58. 1 z^5 + 3 z^2 + 2 z 2 - 14 z^5 + 2 z^2 - 5 z 2 64. 15 t^3 - 3 t^2 + 2 t 2 - 14 t^3 + 2 t^2 + 3 t 2

12 a^2 + 3 a- 12 - 14 a^2 + 5 a+ 62 1 q^4 - 2 q^2 + 102 - 13 q^4 + 5 q^2 - 52

13 r+ 82 - 12 r- 52 12 d+ 72 - 13 d- 12

1 y^3 + 3 y+ 22 + 14 y^3 - 3 y^2 + 2 y- 12 12 x^5 - 2 x^4 +x^3 - 12 + 1 x^4 - 3 x^3 + 22

16 t^2 - 4 t^4 - t 2 + 13 t^4 - 4 t^2 + 52 13 p^2 + 2 p- 52 + 17 p^2 - 4 p^3 + 3 p 2

15 x^2 + 7 x- 42 + 13 x^2 - 6 x+ 22 14 k^3 +k^2 +k 2 + 12 k^3 - 4 k^2 - 3 k 2