Beginning Algebra, 11th Edition

11

The answer is x^2 +^32 x+^94 + 4 x^11 - 4. NOW TRY

9 x- 9

9 x+ 2

6 x^2 - 6 x

6 x^2 + 3 x

4 x^3 - 4 x^2

4 x- 4  4 x^3 + 2 x^2 + 3 x+ 2

9 x

4 x=

9

x 4

(^2) +^3

2 x+

9

4

6 x^2

4 x =

3

2 x

Complete solution available
on the Video Resources on DVD

5.7 EXERCISES

Concept Check Fill in each blank with the correct response.

1.In the statement is the dividend, is the divisor, and

is the quotient.

2.The expression is undefined if.

3.To check the division shown in Exercise 1,multiply by and show that the

product is.

4.The expression a polynomial.

(is/is not)

5.Explain why the division problem can be performed by using the methods of

this section, while the division problem cannot.

6.Concept Check A polynomial in the variable xhas degree 6 and is divided by a mono-

mial in the variable xhaving degree 4. What is the degree of the quotient?

Perform each division. See Examples 1–3.

7. 
   
   
   
   8. 
      
      
      
      9. 
         
      
      
      
      
   
   
   
   

10. 11. 12.

13. 14. 15.

16. 17. 18.

Divide each polynomial by. See Examples 1–3.

19. 
    
    
    
    20. 
        
        
        
        21. 
            
        
        
        
        
    
    
    
    


20. 
    
    
    
    23. 
        
        
        
        24. 
            
        
        
        
        
    
    
    
    


21. 4 x^4 + 3 x^3 + 2 x 26. 5 x^4 - 6 x^3 + 8 x 27.- 81 x^5 + 30 x^4 + 12 x^2

3 x^2 - 18 x^4 + 30 x^536 x+ 24 x^2 + 6 x^39 x- 12 x^2 + 9 x^3

12 x^5 - 9 x^4 + 6 x^324 x^6 - 12 x^5 + 30 x^43 x^2 + 15 x^3 - 27 x^4

3 x^2

• 13 t^9 + 8 t^6 - t^5
  
  
  • t^6
  
  
  
  


• 7 r^7 + 6 r^5 - r^4


• r^5

32 x^8 + 24 x^5 - 8 x^2

• 8 x^2

18 p^5 + 12 p^3 - 6 p^2

• 6 p^3

5 t^8 + 5 t^7 + 15

5 t

4 a^5 - 4 a^2 + 8

4 a

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

2 r

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

2 t

12 t^5 - 6 t^3 + 6 t^2

6 t^2

20 m^5 - 10 m^4 + 5 m^2

5 m^2

120 x^6 - 60 x^3 + 80 x^2

2 x

60 x^4 - 20 x^2 + 10 x

2 x

4 m

16 m^3 - 12 m^2

16 m^3 - 12 m^2

4 m

5 x^2 - 4 x+ 6 +^2 x

3 x+x (^13) x=
10 x^2 + 8
2 =^5 x
(^2) +4,
NOW TRY
EXERCISE 9
Divide
by 2x+4.
10 x^3 + 21 x^2 + 5 x- 8
NOW TRY ANSWER

9. 5 x^2 +^12 x+^32 + 2 x-^14 + 4

346 CHAPTER 5 Exponents and Polynomials

Dividing a Polynomial When the Quotient Has

Fractional Coefficients

Divide by 4 4 x^3 + 2 x^2 + 3 x+ 2 x- 4.

EXAMPLE 9

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