Beginning Algebra, 11th Edition

390 CHAPTER 6 Factoring and Applications

Match each polynomial in Column I with the best choice for factoring it in Column II. The

choices in Column II may be used once, more than once, or not at all.

I

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.z^2 - 24 z+ 144

4 w^2 + 49

x^6 + 4 x^4 - 3 x^2 - 12

8 r^3 - 125

z^2 - 4 z+ 6

36 p^2 - 60 pq+ 25 q^2

64 a^2 - 121 b^2

16 m^2 n+ 24 mn- 40 mn^2

x^2 - 17 x+ 72

12 x^2 + 20 x+ 8

II

A.Factor out the GCF. No further factoring is possible.

B. Factor a difference of squares.

C.Factor a difference of cubes.

D. Factor a sum of cubes.

E. Factor a perfect square trinomial.

F. Factor by grouping.

G.Factor out the GCF. Then factor a trinomial by

grouping or trial and error.

H.Factor into two binomials by finding two integers

whose product is the constant in the trinomial and

whose sum is the coefficient of the middle term.

I. The polynomial is prime.

Factor each polynomial completely.

11. 
    
    
    
    12. 
        
    
    
    
    


12. 
    
    
    
    14. 
        
    
    
    
    


13. 
    
    
    
    16. 
        
    
    
    
    


14. 
    
    
    
    18. 
        
    
    
    
    


15. 
    
    
    
    20. 
        
    
    
    
    


16. 
    
    
    
    22. 
        
    
    
    
    


17. 
    
    
    
    24. 
        
    
    
    
    


18. 
    
    
    
    26. 
        
    
    
    
    


19. 
    
    
    
    28. 
        
    
    
    
    


20. 
    
    
    
    30. 
        
    
    
    
    


21. 
    
    
    
    32. 
        
    
    
    
    


22. 
    
    
    
    34. 
        
    
    
    
    


23. 
    
    
    
    36. 
        
    
    
    
    


24. 
    
    
    
    38. 
        
    
    
    
    


25. 
    
    
    
    40. 
        
    
    
    
    


26. 
    
    
    
    42. 
        
    
    
    
    


27. 
    
    
    
    44. 
        
    
    
    
    


28. 
    
    
    
    46. 
        
    
    
    
    


29. 
    
    
    
    48. 
        
    
    
    
    


30. 
    
    
    
    50. 
        
    
    
    
    


31. 
    
    
    
    52. 
        
    
    
    
    


32. 
    
    
    
    54. 
        
    
    
    
    


33. 
    
    
    
    56. 
        
    
    
    
    


34. 
    
    
    
    58. 59.k^2 - 11 k+ 30 60. 64 p^2 - 100 m^2
    
    
    
    

15 h^2 + 11 hg- 14 g^25 z^3 - 45 z^2 + 70 z

16 r^2 + 24 rm+ 9 m^2 z^2 - 12 z+ 36

32 m^9 + 16 m^5 + 24 m^38 m^3 + 125

k^2 + 9 27 p^10 - 45 p^9 - 252 p^8

z^3 - 8 y^2 - y- 56

8 m- 16 m^2 k^2 - 16

y^4 - 16 20 y^5 - 30 y^4

14 k^3 + 7 k^2 - 70 k 5 +r- 5 s-rs

3 k^2 + 4 k- 4 45 a^3 b^5 - 60 a^4 b^2 + 75 a^6 b^4

54 m^2 - 24 z^28 m^2 - 2 m- 3

4 k^2 - 12 k+ 9 8 p^2 + 23 p- 3

6 z^2 + 31 z+ 5 12 x^2 + 47 x- 4

6 y^2 - 5 y- 4 m^2 - 81

16 x+ 20 m^2 + 2 m- 15

6 n^2 - 19 n+ 10 9 y^2 + 12 y- 5

x^2 - 4 x- 5 x+ 20 100 n^2 r^2 + 30 nr^3 - 50 n^2 r

z^2 - 3 za- 10 a^250 z^2 - 100

8 a^5 - 8 a^4 - 48 a^38 k^2 - 10 k- 3

17 x^3 y^2 + 51 xy 15 y+ 5

10 z^2 - 7 z- 6 2 m^2 - 10 m- 48

p^2 - 17 p+ 66 z^2 - 6 z+ 7 z- 42

6 a+ 12 b+ 18 c m^2 - 3 mn- 4 n^2

6 y^2 - 6 y- 12 7 y^6 + 14 y^5 - 168 y^4

a^2 - 4 a- 12 a^2 + 17 a+ 72

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