Beginning Algebra, 11th Edition

9.Concept Check Which pair of integers

would be used to rewrite the middle term

when one is factoring

by grouping?

A. 3 B.8,

C. 4 D.6,

10.Concept Check Which pair of integers

would be used to rewrite the middle term

when one is factoring

by grouping?

A.10, 3 B.

C.8, 5 D. -8, - 5

- 10, - 3

20 b^2 - 13 b+ 2

- 6, - 4

- 8, - 3

12 y^2 + 5 y- 2

SECTION 6.3 More on Factoring Trinomials 379

Concept Check Which is the correct factored form of the given polynomial?

11. 
    

A.

B.

12.

A.

B. 13 a- 121 a+ 22

13 a+ 121 a- 22

3 a^2 - 5 a- 2

12 x+ 121 x- 12

12 x- 121 x+ 12

2 x^2 - x- 1

13.

A.

B.

14.

A.

B. 14 c+ 3213 c- 42

16 c- 2212 c+ 62

12 c^2 - 7 c- 12

12 y- 5212 y+ 32

1 y+ 5214 y- 32

4 y^2 + 17 y- 15

Complete each factoring. See Examples 1–7.

15. 
    
    
    
    16. = 13 m- 2 n 21 2
    
    
    
    

9 m^2 + 6 mn- 8 n^2

= 13 a- 4 b 21 2

6 a^2 + 7 ab- 20 b^2

17. 18.

= 31 21 2

= 31 2

3 x^2 + 9 x- 30

= 21 21 2

= 21 2

2 x^2 + 6 x- 8

19. 20.

= 3 r 1 21 2

= 3 r 1 2

15 r^3 - 39 r^2 - 18 r

= 2 z 1 21 2

= 2 z 1 2

4 z^3 - 10 z^2 - 6 z

21.The polynomial does not have 2 as a factor. Explain why the binomial
, then, cannot be a factor of the polynomial.

22.Concept Check On a quiz, a student factored by first factoring out
the common factor 3kto get. Then the student wrote the following.

Her answer

WHAT WENT WRONG?What is the correct factored form?

Factor each trinomial completely. See Examples 1–7.(Hint:In Exercises 55 –58, first write
the trinomial in descending powers and then factor.)

23. 
    
    
    
    24. 
        
    
    
    
    


24. 
    
    
    
    26. 
        
    
    
    
    


25. 
    
    
    
    28. 
        
    
    
    
    


26. 
    
    
    
    30. 
        
    
    
    
    


27. 
    
    
    
    32. 
        
    
    
    
    


28. 
    
    
    
    34. 
        
    
    
    
    


29. 
    
    
    
    36. 
        
    
    
    
    


30. 
    
    
    
    38. 
        
    
    
    
    


31. 
    
    
    
    40. 
        
    
    
    
    


32. 24 x^2 - 42 x+ 9 42. 48 b^2 - 74 b- 10

20 x^2 + 22 x+ 6 36 y^2 + 81 y+ 45

3 x^2 - 15 x+ 16 2 t^2 - 14 t+ 15

20 y^2 - 39 y- 11 10 x^2 - 11 x- 6

8 w^2 - 14 w+ 3 9 p^2 - 18 p+ 8

10 m^2 - 23 m+ 12 6 x^2 - 17 x+ 12

12 s^2 + 11 s- 5 20 x^2 + 11 x- 3

15 m^2 +m- 2 6 x^2 +x- 1

2 y^2 + 7 y+ 6 5 z^2 + 12 z+ 4

3 a^2 + 10 a+ 7 7 r^2 + 8 r+ 1

= 1 k- 521 k+ 12

=k 1 k- 52 + 11 k- 52

=k^2 - 5 k+k- 5

k^2 - 4 k- 5

3 k 1 k^2 - 4 k- 52

3 k^3 - 12 k^2 - 15 k

2 x- 6

12 x^2 + 7 x- 12