Intermediate Algebra (11th edition)

Factor each trinomial. (Hint:Factor out the GCF first.)

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Factor each trinomial. See Example 11.

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60. 6 z^4 +z^2 - 1 63. 16 x^4 + 16 x^2 + 3 64. 9 r^4 + 9 r^2 + 2

p^4 - 10 p^2 + 16 k^4 + 10 k^2 + 9 2 x^4 - 9 x^2 - 18

r^21 r-s 2 - 5 rs 1 s-r 2 - 6 s 21 r-s 2

z^21 z-x 2 - zx 1 x-z 2 - 2 x^21 z-x 2

2 k^215 - y 2 - 7 k 15 - y 2 + 515 - y 2

p^21 p+q 2 + 4 pq 1 p+q 2 + 3 q 21 p+q 2

m^21 m-p 22 - mp 1 m-p 22 - 12 p^21 m-p 22

a^21 a+b 22 - ab 1 a+b 22 - 6 b^21 a+b 22

SECTION 6.3 Special Factoring 333

Find each product. See Section 5.4.

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67. 1 y+ 321 y^2 - 3 y+ 92 70. 13 m- 1219 m^2 + 3 m+ 12

1 p+ 3 q 22 12 z- 722

13 x- 5213 x+ 52 18 m+ 3218 m- 32

PREVIEW EXERCISES

OBJECTIVES

Special Factoring

6.3

1 Factor a difference
of squares.

2 Factor a perfect
square trinomial.

3 Factor a difference
of cubes.

4 Factor a sum of
cubes.

OBJECTIVE 1 Factor a difference of squares.The special products intro-

duced in Section 5.4are used in reverse when factoring. Recall that the product of the

sum and difference of two terms leads to a difference of squares.

Difference of Squares

x^2 y^2  1 xy 21 xy 2

Factoring Differences of Squares

Factor each polynomial.

(a)

Factor the difference of squares.

(b)

Factor out the common factor, 4.

Factor the difference of squares.

(c) 16 m^2 - 49 p^2 = 14 m 22 - 17 p 22 = 14 m+ 7 p 214 m- 7 p 2

x^2 - y^2 = 1 x + y 2 1 x - y 2

= 41 a+ 421 a- 42

= 41 a^2 - 162

4 a^2 - 64

= 1 t+ 621 t- 62

=t^2 - 62 36 = 62

t^2 - 36

EXAMPLE 1