Intermediate Algebra (11th edition)

SECTION 5.4 Multiplying Polynomials 299

Complete solution available
on the Video Resources on DVD

5.4 EXERCISES

Concept Check Match each product in Column I with the correct polynomial in Column II.

III

1. A.


2. B.


3. C.


4. 12 x+ 5213 x- 42 D. 6 x^2 - 23 x+ 20

12 x- 5213 x- 42 6 x^2 - 7 x- 20

12 x+ 5213 x+ 42 6 x^2 + 7 x- 20

12 x- 5213 x+ 42 6 x^2 + 23 x+ 20

23. 24. 25.

2 b+ 4

12 y+ 3213 y- 42 12 m+ 6215 m- 32 - b^2 + 3 b+ 3

26. 27. 28.

2 k- 6 q

2 k+ 6 q

5 m+ 3 n

5 m- 3 n

3 r- 2

• r^2 - 4 r+ 8

29. 30.

2 z- 5

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

4 z+ 3

2 z^3 - 5 z^2 + 8 z- 1

Use the FOIL method to find each product. See Example 4.

33. 
    
    
    
    34. 
        
        
        
        35. 
            
        
        
        
        
    
    
    
    


34. 
    
    
    
    37. 
        
        
        
        38. 
            
        
        
        
        
    
    
    
    


35. 
    
    
    
    40. 41.Describe the FOIL method in your own words.
        42.Explain why the product of the sum and difference of two terms is not a trinomial.
    
    
    
    

16 c-d 212 c+ 3 d 2 12 m-n 213 m+ 5 n 2

15 w+ 2212 w- 52 1 z-w 213 z+ 4 w 2 1 s-t 212 s+ 5 t 2

1 m+ 521 m- 82 1 p+ 421 p- 62 14 k+ 3213 k- 22

Find each product. See Example 5.

43. 
    
    
    
    44. 
        
        
        
        45. 
            
        
        
        
        
    
    
    
    


44. 
    
    
    
    47. 
        
        
        
        48. 
            
        
        
        
        
    
    
    
    


45. 
    
    
    
    50. 
        
        
        
        51. 
            
        
        
        
        
    
    
    
    


46. 12 k^2 + 6 h 212 k^2 - 6 h 2 53. 3 y 15 y^3 + 2215 y^3 - 22 54. 4 x 13 x^3 + 4213 x^3 - 42

13 a+ 2 c 213 a- 2 c 2 15 r+ 4 s 215 r- 4 s 2 14 m+ 7 n^2214 m- 7 n^22

13 x- 8213 x+ 82 15 m- 1215 m+ 12 16 y- 3216 y+ 32

1 x+ 921 x- 92 1 z+ 621 z- 62 12 p- 3212 p+ 32

Find each product. See Example 6.

55. 
    
    
    
    56. 
        
        
        
        57. 
            
            
            
            58. 
                
            
            
            
            
        
        
        
        
    
    
    
    


56. 12 p+ 722 60. 13 z+ 822 61. 14 n- 3 m 22 62. 15 r- 7 s 22

1 y- 522 1 a- 322 1 x+ 122 1 t+ 222

Find each product. See Examples 1–3.

5. 
   
   
   
   6. 
      
      
      
      7. 
         
      
      
      
      
   
   
   
   


6. 
   
   
   
   9. 
      
      
      
      10. 
          
      
      
      
      
   
   
   
   


7. 
   
   
   
   12. 
       
       
       
       13. 
           
       
       
       
       
   
   
   
   


8. 
   
   
   
   15. 
       
       
       
       16. 
           
       
       
       
       
   
   
   
   


9. 
   
   
   
   18. 
       
       
       
       19. 
           
       
       
       
       
   
   
   
   


10. 2 y 12 y+ 1218 y- 32 21. 4 x^31 x- 321 x+ 22 22. 2 y^51 y- 821 y+ 22

m 1 m+ 521 m- 82 p 1 p+ 421 p- 62 4 z 12 z+ 1213 z- 42

5 r^312 r^2 + 3 r+ 42 12 t+ 3213 t^2 - 4 t- 12 14 z+ 221 z^2 - 3 z- 52

• q^312 + 3 q 2 - 3 a^414 +a 2 6 k^213 k^2 + 2 k+ 12

5 m^3 n^41 - 4 m^2 n^523 x 1 - 2 x+ 52 5 y 1 - 6 y+ 12

• 8 m^313 m^22 - 4 p^215 p^4214 x^2 y^31 - 2 x^5 y 2

31. 32.

2 y^2 + y+ 3

5 y^2 - 2 y+ 4

3 p^2 - 4 p- 1

2 p^2 + 3 p+ 6