Intermediate Algebra (11th edition)

(c)

Associative property

Perfect square trinomial

Difference of squares

(d)

Rearrange and

group the terms.

Factor each

group.

Factor out the common

factor.

NOW TRY

2 m-n

= 12 m-n 214 m^2 + 2 mn+ n^2 + 2 m+n 2

= 12 m-n 214 m^2 + 2 mn+ n^22 + 12 m-n 212 m+n 2

= 18 m^3 - n^32 + 14 m^2 - n^22

8 m^3 + 4 m^2 - n^3 - n^2

= 12 a+ 1 + b 212 a+ 1 - b 2

= 12 a+ 122 - b^2

= 14 a^2 + 4 a+ 12 - b^2

4 a^2 + 4 a+ 1 - b^2

342 CHAPTER 6 Factoring

NOW TRY
EXERCISE 4
Factor each polynomial.

(a)

(b)

(c) x^3 - 9 y^2 - 27 y^3 +x^2

9 u^2 - 48 u+ 64 - v^2

5 a^3 + 5 a^2 b-ab^2 - b^3

NOW TRY ANSWERS

4. (a)
   (b)
   (c)
   x+ 3 y 2

1 x- 3 y 21 x^2 + 3 xy+ 9 y^2 +

13 u- 8 +v 213 u- 8 - v 2

1 a+b 215 a^2 - b^22

Complete solution available
on the Video Resources on DVD

6.4 EXERCISES

The following exercises are of mixed variety. Factor each polynomial. See Examples 1– 4.

1. 
   
   
   
   2. 
      
   
   
   
   


2. 
   
   
   
   4. 
      
   
   
   
   


3. 
   
   
   
   6. 
      
   
   
   
   


4. 
   
   
   
   8. 
      
   
   
   
   


5. 
   
   
   
   10. 
       
   
   
   
   


6. 
   
   
   
   12. 
       
   
   
   
   


7. 
   
   
   
   14. 
       
   
   
   
   


8. 
   
   
   
   16. 
       
   
   
   
   


9. 
   
   
   
   18. 
       
   
   
   
   


10. 
    
    
    
    20. 
        
    
    
    
    


11. 
    
    
    
    22. 
        
    
    
    
    


12. 
    
    
    
    24. 
        
    
    
    
    


13. 
    
    
    
    26. 
        
    
    
    
    


14. 
    
    
    
    28. 
        
    
    
    
    


15. 
    
    
    
    30. 
        
    
    
    
    


16. 
    
    
    
    32. 
        
    
    
    
    


17. 
    
    
    
    34. 
        
    
    
    
    


18. 
    
    
    
    36. 
        
    
    
    
    


19. 
    
    
    
    38. 
        
    
    
    
    


20. 
    
    
    
    40. 41.^24 p^3 q+^52 p^2 q^2 +^20 pq^3 42. 32 x^2 +^16 x^3 -^24 x^5
    
    
    
    

10 r^2 + 23 rs- 5 s 2 12 k^2 - 17 kq- 5 q 2

512 + 1000 z^364 m^2 - 25 n^2

256 b^2 - 400 c^2 z^2 - zp- 20 p^2

12 z^3 - 6 z^2 + 18 z 225 k^2 - 36 r^2

64 m^2 - 625 14 z^2 - 3 zk- 2 k^2

p^3 + 1 48 y^2 z^3 - 28 y^3 z^4

625 - x^42 m^2 - mn- 15 n 2

x^2 + 2 x- 35 9 - a^2 + 2 ab-b^2

16 z^3 x^2 - 32 z^2 x 9 r^2 + 100

kq- 9 q+kr- 9 r 56 k^3 - 875

9 m^2 - 30 mn+ 25 n^22 a^2 - 7 a- 4

54 m^3 - 2000 mn- 2 n+ 5 m- 10

9 m^2 - 45 m+ 18 m^34 k^2 + 28 kr+ 49 r^2

41 p+ 22 +m 1 p+ 22 40 p- 32 r

x^3 - 1000 6 t^2 + 19 tu- 77 u 2

6 b^2 - 17 b- 3 k^2 - 6 k- 16

225 p^2 + 256 18 m^3 n+ 3 m^2 n^2 - 6 mn^3

3 a^2 pq+ 3 abpq- 90 b^2 pq 49 z^2 - 16

3 p^4 - 3 p^3 - 90 p^2 k^4 - 16

100 a^2 - 9 b^210 r^2 + 13 r- 3

Difference

of cubes

Difference

of squares