Beginning Algebra, 11th Edition

68.Concept Check A student factored as follows.

The student could not find a common factor of the two terms. WHAT WENT WRONG?
Complete the factoring.

Factor by grouping. See Examples 5 and 6.

89.a^5 - 3 + 2 a^5 b- 6 b 90.b^3 - 2 + 5 ab^3 - 10 a

18 r^2 - 2 ty+ 12 ry- 3 rt 12 a^2 - 4 bc+ 16 ac- 3 ab

5 m- 6 p- 2 mp+ 15 7 y- 9 x- 3 xy+ 21

y^2 + 3 x+ 3 y+xy m^2 + 14 p+ 7 m+ 2 mp

16 m^3 - 4 m^2 p^2 - 4 mp+p^310 t^3 - 2 t^2 s^2 - 5 ts+s^3

12 - 4 a- 3 b+ab 6 - 3 x- 2 y+xy

3 a^3 + 3 ab^2 + 2 a^2 b+ 2 b^34 x^3 + 3 x^2 y+ 4 xy^2 + 3 y^3

18 r^2 + 12 ry- 3 xr- 2 xy 8 s^2 - 4 st+ 6 sy- 3 yt

7 z^2 + 14 z-az- 2 a 5 m^2 + 15 mp- 2 mr- 6 pr

a^2 - 2 a+ab- 2 b y^2 - 6 y+yw- 6 w

p^2 + 4 p+pq+ 4 q m^2 + 2 m+mn+ 2 n

=x^21 x+ 42 + 21 - x- 42

= 1 x^3 + 4 x^22 + 1 - 2 x- 82

x^3 + 4 x^2 - 2 x- 8

x^3 + 4 x^2 - 2 x- 8

SECTION 6.1 The Greatest Common Factor; Factoring by Grouping 367

EXERCISES 91–94

FOR INDIVIDUAL OR GROUP WORK

In many cases, the choice of which pairs of terms to group when factoring by grouping

can be made in different ways. To see this for Example 6 ( b), work Exercises 91–94 in

order.

91.Start with the polynomial from Example 6 (b), and rearrange

the terms as follows:

What property from Section 1.7allows this?

92.Group the first two terms and the last two terms of the rearranged polynomial in

Exercise 91.Then factor each group.

93.Is your result from Exercise 92in factored form? Explain your answer.

94.If your answer to Exercise 93is no,factor the polynomial. Is the result the same as

that shown for Example 6 (b)?

2 xy- 8 x- 3 y+12.

2 xy+ 12 - 3 y- 8 x,

RELATING CONCEPTS

Find each product. See Section 5.5.

95. 
    
    
    
    96. 
        
    
    
    
    


96. 
    
    
    
    98. 
        
    
    
    
    


97. 2 x^21 x^2 + 3 x+ 52 100. - 5 x^212 x^2 - 4 x- 92

1 x+ 221 x+ 72 2 x 1 x+ 521 x- 12

1 x+ 621 x- 92 1 x- 321 x- 62

PREVIEW EXERCISES