Beginning Algebra, 11th Edition

Although we usually factor polynomials using integers, we can apply the same concepts to

factoring using fractions and decimals.

Factor the difference of squares.

Apply the special factoring rules of this section to factor each binomial or trinomial.

83. 
    
    
    
    84. 
        
        
        
        85. 
            
        
        
        
        
    
    
    
    

86. 87. 88.

89. 90. 91.

92. 93. 94.

Brain Busters Factor each polynomial completely.

95. 
    
    
    
    96. 97.m^2 - p^2 + 2 m+ 2 p 98. 3 r- 3 k+ 3 r^2 - 3 k^2
    
    
    
    

1 m+n 22 - 1 m-n 22 1 a-b 23 - 1 a+b 23

x^3 +

1

64

x^3 +

1

8

y^2 - 1.4y+0.49

m^2 + x^2 - 1.0x+0.25

2

3

m+

1

9

t^2 +t+

1

4

100 b^2 - x^2 - 0.64 y^2 - 0.36

4

49

36 m^2 -

16

25

q^2 -

1

4

p^2 -

1

9

=az+

3

4

baz-

3

4

b

9

16 =A

3

4 B

=z^2 - a^32

4

b

2

z^2 -

9

16

Summary Exercises on Factoring 389

Solve each equation. See Sections 2.1 and 2.2.

99.m- 4 = 0 100. 3 t+ 2 = 0 101. 2 t+ 10 = 0 102. 7 x= 0

PREVIEW EXERCISES

As you factor a polynomial, ask yourself these questions to decide on a suitable

factoring technique.

SUMMARY EXERCISESon Factoring

Factoring a Polynomial

1. Is there a common factor?If so, factor it out.


2. How many terms are in the polynomial?
   Two terms:Check to see whether it is a difference of squares or a sum
   or difference of cubes. If so, factor as in Section 6.4.
   Three terms:Is it a perfect square trinomial? If the trinomial is not a
   perfect square, check to see whether the coefficient of the second-
   degree term is 1. If so, use the method of Section 6.2.If the coefficient
   of the second-degree term of the trinomial is not 1, use the general fac-
   toring methods of Section 6.3.
   Four terms:Try to factor the polynomial by grouping, as in Section 6.1.


3. Can any factors be factored further?If so, factor them.

(continued)