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6.1

2 · 2 · 2 · 7 2 · 2 · 2 · 7

6.2

72

6.3

−21 a 2 24 a b −21 a 2 24 a b

6.4

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

6.5

6 y 2 + 23 y + 20 6 y 2 + 23 y + 20

6.6

−54, 54

6.7

27 x 6 27 x 6

6.8

m 2 + 8 m + 16 m 2 + 8 m + 16

6.9

x 2 9 x 2 9

6.10

y = 3 5 y = 3 5

6.11

n ( n 11 ) ( n + 2 ) n ( n 11 ) ( n + 2 )

6.12

8 ; x = 2 8 ; x = 2

Try It

6.1

5 m 2 5 m 2

6.2

7 x 7 x

6.3

3 y 2 ( 3 x + 2 x 2 + 7 y ) 3 y 2 ( 3 x + 2 x 2 + 7 y )

6.4

3 p ( p 2 2 p q + 3 q 2 ) 3 p ( p 2 2 p q + 3 q 2 )

6.5

2 x 2 ( x + 6 ) 2 x 2 ( x + 6 )

6.6

3 y 2 ( 2 y 5 ) 3 y 2 ( 2 y 5 )

6.7

3 x y ( 5 x 2 x y + 2 y 2 ) 3 x y ( 5 x 2 x y + 2 y 2 )

6.8

2 a b ( 4 a 2 + a b 3 b 2 ) 2 a b ( 4 a 2 + a b 3 b 2 )

6.9

−4 b ( b 2 4 b + 2 ) −4 b ( b 2 4 b + 2 )

6.10

−7 a ( a 2 3 a + 2 ) −7 a ( a 2 3 a + 2 )

6.11

( m + 3 ) ( 4 m 7 ) ( m + 3 ) ( 4 m 7 )

6.12

( n 4 ) ( 8 n + 5 ) ( n 4 ) ( 8 n + 5 )

6.13

( x + 8 ) ( y + 3 ) ( x + 8 ) ( y + 3 )

6.14

( a + 7 ) ( b + 8 ) ( a + 7 ) ( b + 8 )

6.15

(x5)(x+2)(x5)(x+2)
(5x4)(4x3)(5x4)(4x3)

6.16

(y+4)(y7)(y+4)(y7)
(7m3)(6m5)(7m3)(6m5)

6.17

( q + 4 ) ( q + 6 ) ( q + 4 ) ( q + 6 )

6.18

( t + 2 ) ( t + 12 ) ( t + 2 ) ( t + 12 )

6.19

( u 3 ) ( u 6 ) ( u 3 ) ( u 6 )

6.20

( y 7 ) ( y 9 ) ( y 7 ) ( y 9 )

6.21

( m + 3 ) ( m + 6 ) ( m + 3 ) ( m + 6 )

6.22

( n 3 ) ( n 4 ) ( n 3 ) ( n 4 )

6.23

( a b ) ( a 10 b ) ( a b ) ( a 10 b )

6.24

( m n ) ( m 12 n ) ( m n ) ( m 12 n )

6.25

prime

6.26

prime

6.27

5 x ( x 1 ) ( x + 4 ) 5 x ( x 1 ) ( x + 4 )

6.28

6 y ( y 2 ) ( y + 5 ) 6 y ( y 2 ) ( y + 5 )

6.29

( a + 1 ) ( 2 a + 3 ) ( a + 1 ) ( 2 a + 3 )

6.30

( b + 1 ) ( 4 b + 1 ) ( b + 1 ) ( 4 b + 1 )

6.31

( 2 x 3 ) ( 4 x 1 ) ( 2 x 3 ) ( 4 x 1 )

6.32

( 2 y 7 ) ( 5 y 1 ) ( 2 y 7 ) ( 5 y 1 )

6.33

( 3 x + 2 y ) ( 6 x 5 y ) ( 3 x + 2 y ) ( 6 x 5 y )

6.34

( 3 x + y ) ( 10 x 21 y ) ( 3 x + y ) ( 10 x 21 y )

6.35

5 n ( n 4 ) ( 3 n 5 ) 5 n ( n 4 ) ( 3 n 5 )

6.36

8 q ( q + 6 ) ( 7 q 2 ) 8 q ( q + 6 ) ( 7 q 2 )

6.37

( x + 2 ) ( 6 x + 1 ) ( x + 2 ) ( 6 x + 1 )

6.38

( 2 y + 1 ) ( 2 y + 3 ) ( 2 y + 1 ) ( 2 y + 3 )

6.39

4 ( 2 x 3 ) ( 2 x 1 ) 4 ( 2 x 3 ) ( 2 x 1 )

6.40

3 ( 3 w 2 ) ( 2 w 3 ) 3 ( 3 w 2 ) ( 2 w 3 )

6.41

( h 2 2 ) ( h 2 + 6 ) ( h 2 2 ) ( h 2 + 6 )

6.42

( y 2 + 4 ) ( y 2 5 ) ( y 2 + 4 ) ( y 2 5 )

6.43

( x 3 ) ( x 1 ) ( x 3 ) ( x 1 )

6.44

( y 1 ) ( y + 1 ) ( y 1 ) ( y + 1 )

6.45

( 2 x + 3 ) 2 ( 2 x + 3 ) 2

6.46

( 3 y + 4 ) 2 ( 3 y + 4 ) 2

6.47

( 8 y 5 ) 2 ( 8 y 5 ) 2

6.48

( 4 z 9 ) 2 ( 4 z 9 ) 2

6.49

( 7 x + 6 y ) 2 ( 7 x + 6 y ) 2

6.50

( 8 m + 7 n ) 2 ( 8 m + 7 n ) 2

6.51

2 y ( 2 x 3 ) 2 2 y ( 2 x 3 ) 2

6.52

3 q ( 3 p + 5 ) 2 3 q ( 3 p + 5 ) 2

6.53

( 11 m 1 ) ( 11 m + 1 ) ( 11 m 1 ) ( 11 m + 1 )

6.54

( 9 y 1 ) ( 9 y + 1 ) ( 9 y 1 ) ( 9 y + 1 )

6.55

( 14 m 5 n ) ( 14 m + 5 n ) ( 14 m 5 n ) ( 14 m + 5 n )

6.56

( 11 p 3 q ) ( 11 p + 3 q ) ( 11 p 3 q ) ( 11 p + 3 q )

6.57

2 y 2 ( x 2 ) ( x + 2 ) ( x 2 + 4 ) 2 y 2 ( x 2 ) ( x + 2 ) ( x 2 + 4 )

6.58

7 c 2 ( a b ) ( a + b ) ( a 2 + b 2 ) 7 c 2 ( a b ) ( a + b ) ( a 2 + b 2 )

6.59

( x 5 y ) ( x 5 + y ) ( x 5 y ) ( x 5 + y )

6.60

( x + 3 2 y ) ( x + 3 + 2 y ) ( x + 3 2 y ) ( x + 3 + 2 y )

6.61

( x + 3 ) ( x 2 3 x + 9 ) ( x + 3 ) ( x 2 3 x + 9 )

6.62

( y + 2 ) ( y 2 2 y + 4 ) ( y + 2 ) ( y 2 2 y + 4 )

6.63

( 2 x 3 y ) ( 4 x 2 + 6 x y + 9 y 2 ) ( 2 x 3 y ) ( 4 x 2 + 6 x y + 9 y 2 )

6.64

125 ( 2 m n ) ( 4 m 2 + 2 m n + n 2 ) 125 ( 2 m n ) ( 4 m 2 + 2 m n + n 2 )

6.65

4 ( 5 p + q ) ( 25 p 2 5 p q + q 2 ) 4 ( 5 p + q ) ( 25 p 2 5 p q + q 2 )

6.66

2 ( 6 c + 7 d ) ( 36 c 2 42 c d + 49 d 2 ) 2 ( 6 c + 7 d ) ( 36 c 2 42 c d + 49 d 2 )

6.67

( −2 y + 1 ) ( 13 y 2 + 5 y + 1 ) ( −2 y + 1 ) ( 13 y 2 + 5 y + 1 )

6.68

( −4 n + 3 ) ( 31 n 2 + 21 n + 9 ) ( −4 n + 3 ) ( 31 n 2 + 21 n + 9 )

6.69

8 y ( y 1 ) ( y + 3 ) 8 y ( y 1 ) ( y + 3 )

6.70

5 y ( y 9 ) ( y + 6 ) 5 y ( y 9 ) ( y + 6 )

6.71

4 x ( 2 x 3 ) ( 2 x + 3 ) 4 x ( 2 x 3 ) ( 2 x + 3 )

6.72

3 ( 3 y 4 ) ( 3 y + 4 ) 3 ( 3 y 4 ) ( 3 y + 4 )

6.73

( 2 x + 5 y ) 2 ( 2 x + 5 y ) 2

6.74

( 3 x 4 y ) 2 ( 3 x 4 y ) 2

6.75

2 x y ( 25 x 2 + 36 ) 2 x y ( 25 x 2 + 36 )

6.76

3 x y ( 9 y 2 + 16 ) 3 x y ( 9 y 2 + 16 )

6.77

2 ( 5 m + 6 n ) ( 25 m 2 30 m n + 36 n 2 ) 2 ( 5 m + 6 n ) ( 25 m 2 30 m n + 36 n 2 )

6.78

2 ( p + 3 q ) ( p 2 3 p q + 9 q 2 ) 2 ( p + 3 q ) ( p 2 3 p q + 9 q 2 )

6.79

4 a b ( a 2 + 4 ) ( a 2 ) ( a + 2 ) 4 a b ( a 2 + 4 ) ( a 2 ) ( a + 2 )

6.80

7 x y ( y 2 + 1 ) ( y 1 ) ( y + 1 ) 7 x y ( y 2 + 1 ) ( y 1 ) ( y + 1 )

6.81

6 ( x + b ) ( x 2 c ) 6 ( x + b ) ( x 2 c )

6.82

2 ( 4 x 1 ) ( 2 x + 3 y ) 2 ( 4 x 1 ) ( 2 x + 3 y )

6.83

4 q ( p 3 ) ( p 1 ) 4 q ( p 3 ) ( p 1 )

6.84

3 p ( 2 q + 1 ) ( q 2 ) 3 p ( 2 q + 1 ) ( q 2 )

6.85

( 2 x 3 y 5 ) ( 2 x 3 y + 5 ) ( 2 x 3 y 5 ) ( 2 x 3 y + 5 )

6.86

( 4 x 3 y 8 ) ( 4 x 3 y + 8 ) ( 4 x 3 y 8 ) ( 4 x 3 y + 8 )

6.87

m = 2 3 , m = 1 2 m = 2 3 , m = 1 2

6.88

p = 3 4 , p = 3 4 p = 3 4 , p = 3 4

6.89

c = 2 , c = 4 3 c = 2 , c = 4 3

6.90

d = 3 , d = 1 2 d = 3 , d = 1 2

6.91

p = 7 5 , p = 7 5 p = 7 5 , p = 7 5

6.92

x = 11 6 , x = 11 6 x = 11 6 , x = 11 6

6.93

m = 1 , m = 3 2 m = 1 , m = 3 2

6.94

k = 3 , k = −3 k = 3 , k = −3

6.95

a = 5 2 , a = 2 3 a = 5 2 , a = 2 3

6.96

b = −2 , b = 1 20 b = −2 , b = 1 20

6.97

x = 0 , x = 3 2 x = 0 , x = 3 2

6.98

y = 0 , y = 1 4 y = 0 , y = 1 4

6.99

x=−3x=−3 or x=5x=5
(−3,7)(−3,7) (5,7)(5,7)

6.100

x=1x=1 or x=7x=7
(1,−4)(1,−4) (7,−4)(7,−4)

6.101

x=1x=1 or x=52x=52
(1,0),(1,0), (52,0)(52,0) (0,5)(0,5)

6.102

x=−3x=−3 or x=56x=56
(−3,0),(−3,0), (56,0)(56,0) (0,−15)(0,−15)

6.103

−15,−17−15,−17 and 15, 17

6.104

−23,−21−23,−21 and 21, 23

6.105

The width is 5 feet and length is 6 feet.

6.106

The width of the patio is 12 feet and the length is 15 feet.

6.107

5 feet and 12 feet

6.108

The other leg is 24 feet and the hypotenuse is 25 feet.

6.109

5 seconds; 0 and 3 seconds; 196 feet

6.110

4 seconds; 0 and 2 seconds; 144 feet

Section 6.1 Exercises

1.

2 p q 2 p q

3.

6 m 2 n 3 6 m 2 n 3

5.

2 a 2 a

7.

5 x 3 y 5 x 3 y

9.

3 ( 2 m + 3 ) 3 ( 2 m + 3 )

11.

9 ( n 7 ) 9 ( n 7 )

13.

3 ( x 2 + 2 x 3 ) 3 ( x 2 + 2 x 3 )

15.

2 ( 4 p 2 + 2 p + 1 ) 2 ( 4 p 2 + 2 p + 1 )

17.

8 y 2 ( y + 2 ) 8 y 2 ( y + 2 )

19.

5 x ( x 2 3 x + 4 ) 5 x ( x 2 3 x + 4 )

21.

3 x ( 8 x 2 4 x + 5 ) 3 x ( 8 x 2 4 x + 5 )

23.

6 y 2 ( 2 x + 3 x 2 5 y ) 6 y 2 ( 2 x + 3 x 2 5 y )

25.

4 x y ( 5 x 2 x y + 3 y 2 ) 4 x y ( 5 x 2 x y + 3 y 2 )

27.

−2 ( x + 2 ) −2 ( x + 2 )

29.

−2 x ( x 2 9 x + 4 ) −2 x ( x 2 9 x + 4 )

31.

−4 p q ( p 2 + 3 p q 4 q ) −4 p q ( p 2 + 3 p q 4 q )

33.

( x + 1 ) ( 5 x + 3 ) ( x + 1 ) ( 5 x + 3 )

35.

( b 2 ) ( 3 b 13 ) ( b 2 ) ( 3 b 13 )

37.

( b + 5 ) ( a + 3 ) ( b + 5 ) ( a + 3 )

39.

( y + 5 ) ( 8 y + 1 ) ( y + 5 ) ( 8 y + 1 )

41.

( u + 2 ) ( v 9 ) ( u + 2 ) ( v 9 )

43.

( u 1 ) ( u + 6 ) ( u 1 ) ( u + 6 )

45.

( 3 p 5 ) ( 3 p + 4 ) ( 3 p 5 ) ( 3 p + 4 )

47.

( n 6 ) ( m 4 ) ( n 6 ) ( m 4 )

49.

( x 7 ) ( 2 x 5 ) ( x 7 ) ( 2 x 5 )

51.

−9 x y ( 2 y + 3 x ) −9 x y ( 2 y + 3 x )

53.

( x 2 + 2 ) ( 3 x 7 ) ( x 2 + 2 ) ( 3 x 7 )

55.

( x + y ) ( x + 5 ) ( x + y ) ( x + 5 )

57.

Answers will vary.

59.

Answers will vary.

Section 6.2 Exercises

61.

( p + 5 ) ( p + 6 ) ( p + 5 ) ( p + 6 )

63.

( n + 3 ) ( n + 16 ) ( n + 3 ) ( n + 16 )

65.

( a + 5 ) ( a + 20 ) ( a + 5 ) ( a + 20 )

67.

( x 2 ) ( x 6 ) ( x 2 ) ( x 6 )

69.

( y 3 ) ( y 15 ) ( y 3 ) ( y 15 )

71.

( x 1 ) ( x 7 ) ( x 1 ) ( x 7 )

73.

( p 1 ) ( p + 6 ) ( p 1 ) ( p + 6 )

75.

( x 4 ) ( x 2 ) ( x 4 ) ( x 2 )

77.

( x 12 ) ( x + 1 ) ( x 12 ) ( x + 1 )

79.

( x + 8 y ) ( x 10 y ) ( x + 8 y ) ( x 10 y )

81.

( m + n ) ( m 65 n ) ( m + n ) ( m 65 n )

83.

( a + 8 b ) ( a 3 b ) ( a + 8 b ) ( a 3 b )

85.

Prime

87.

Prime

89.

p ( p 10 ) ( p + 2 ) p ( p 10 ) ( p + 2 )

91.

3 m ( m 5 ) ( m 2 ) 3 m ( m 5 ) ( m 2 )

93.

5 x 2 ( x 3 ) ( x + 5 ) 5 x 2 ( x 3 ) ( x + 5 )

95.

( 2 t + 5 ) ( t + 1 ) ( 2 t + 5 ) ( t + 1 )

97.

( 11 x + 1 ) ( x + 3 ) ( 11 x + 1 ) ( x + 3 )

99.

( 4 w 1 ) ( w 1 ) ( 4 w 1 ) ( w 1 )

101.

( 4 q + 1 ) ( q 2 ) ( 4 q + 1 ) ( q 2 )

103.

( 2 p 5 q ) ( 3 p 2 q ) ( 2 p 5 q ) ( 3 p 2 q )

105.

( 4 a 3 b ) ( a + 5 b ) ( 4 a 3 b ) ( a + 5 b )

107.

−16 ( x + 1 ) ( x + 1 ) −16 ( x + 1 ) ( x + 1 )

109.

−10 q ( 3 q + 2 ) ( q + 4 ) −10 q ( 3 q + 2 ) ( q + 4 )

111.

( 5 n + 1 ) ( n + 4 ) ( 5 n + 1 ) ( n + 4 )

113.

( 2 k 3 ) ( 2 k 5 ) ( 2 k 3 ) ( 2 k 5 )

115.

( 3 y + 5 ) ( 2 y 3 ) ( 3 y + 5 ) ( 2 y 3 )

117.

( 2 n + 3 ) ( n 15 ) ( 2 n + 3 ) ( n 15 )

119.

10 ( 6 y 1 ) ( y + 5 ) 10 ( 6 y 1 ) ( y + 5 )

121.

3 z ( 8 z + 3 ) ( 2 z 5 ) 3 z ( 8 z + 3 ) ( 2 z 5 )

123.

8 ( 2 s + 3 ) ( s + 1 ) 8 ( 2 s + 3 ) ( s + 1 )

125.

12 ( 4 y 3 ) ( y + 1 ) 12 ( 4 y 3 ) ( y + 1 )

127.

( x 2 + 1 ) ( x 2 7 ) ( x 2 + 1 ) ( x 2 7 )

129.

( x 2 7 ) ( x 2 + 4 ) ( x 2 7 ) ( x 2 + 4 )

131.

( x 12 ) ( x + 1 ) ( x 12 ) ( x + 1 )

133.

( 3 y 4 ) ( 3 y 1 ) ( 3 y 4 ) ( 3 y 1 )

135.

( u 6 ) ( u 6 ) ( u 6 ) ( u 6 )

137.

( r 4 s ) ( r 16 s ) ( r 4 s ) ( r 16 s )

139.

( 4 y 7 ) ( 3 y 2 ) ( 4 y 7 ) ( 3 y 2 )

141.

( 2 n 1 ) ( 3 n + 4 ) ( 2 n 1 ) ( 3 n + 4 )

143.

13 ( z 2 + 3 z 2 ) 13 ( z 2 + 3 z 2 )

145.

3 p ( p + 7 ) 3 p ( p + 7 )

147.

6 ( r + 2 ) ( r + 3 ) 6 ( r + 2 ) ( r + 3 )

149.

4 ( 2 n + 1 ) ( 3 n + 1 ) 4 ( 2 n + 1 ) ( 3 n + 1 )

151.

( x 2 + 2 ) ( x 2 6 ) ( x 2 + 2 ) ( x 2 6 )

153.

( x 9 ) ( x + 6 ) ( x 9 ) ( x + 6 )

155.

Answers will vary.

157.

Answers will vary.

Section 6.3 Exercises

159.

( 4 y + 3 ) 2 ( 4 y + 3 ) 2

161.

( 6 s + 7 ) 2 ( 6 s + 7 ) 2

163.

( 10 x 1 ) 2 ( 10 x 1 ) 2

165.

( 5 n 12 ) 2 ( 5 n 12 ) 2

167.

( 7 x + 2 y ) 2 ( 7 x + 2 y ) 2

169.

( 10 y 1 ) 2 ( 10 y 1 ) 2

171.

10 j ( k + 4 ) 2 10 j ( k + 4 ) 2

173.

3 u 2 ( 5 u v ) 2 3 u 2 ( 5 u v ) 2

175.

( 5 v 1 ) ( 5 v + 1 ) ( 5 v 1 ) ( 5 v + 1 )

177.

( 2 7 x ) ( 2 + 7 x ) ( 2 7 x ) ( 2 + 7 x )

179.

6 p 2 ( q 3 ) ( q + 3 ) 6 p 2 ( q 3 ) ( q + 3 )

181.

6 ( 4 p 2 + 9 ) 6 ( 4 p 2 + 9 )

183.

( 11 x 12 y ) ( 11 x + 12 y ) ( 11 x 12 y ) ( 11 x + 12 y )

185.

( 13 c 6 d ) ( 13 c + 6 d ) ( 13 c 6 d ) ( 13 c + 6 d )

187.

( 2 z 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 ) ( 2 z 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 )

189.

2 b 2 ( 3 a 2 ) ( 3 a + 2 ) ( 9 a 2 + 4 ) 2 b 2 ( 3 a 2 ) ( 3 a + 2 ) ( 9 a 2 + 4 )

191.

( x 8 y ) ( x 8 + y ) ( x 8 y ) ( x 8 + y )

193.

( a + 3 3 b ) ( a + 3 + 3 b ) ( a + 3 3 b ) ( a + 3 + 3 b )

195.

( x + 5 ) ( x 2 5 x + 25 ) ( x + 5 ) ( x 2 5 x + 25 )

197.

( z 2 3 ) ( z 4 + 3 z 2 + 9 ) ( z 2 3 ) ( z 4 + 3 z 2 + 9 )

199.

( 2 7 t ) ( 4 + 14 t + 49 t 2 ) ( 2 7 t ) ( 4 + 14 t + 49 t 2 )

201.

( 2 y 5 z ) ( 4 y 2 + 10 y z + 25 z 2 ) ( 2 y 5 z ) ( 4 y 2 + 10 y z + 25 z 2 )

203.

( 6 a + 5 b ) ( 36 a 2 30 a b + 25 b 2 ) ( 6 a + 5 b ) ( 36 a 2 30 a b + 25 b 2 )

205.

7 ( k + 2 ) ( k 2 2 k + 4 ) 7 ( k + 2 ) ( k 2 2 k + 4 )

207.

2 x 2 ( 1 2 y ) ( 1 + 2 y + 4 y 2 ) 2 x 2 ( 1 2 y ) ( 1 + 2 y + 4 y 2 )

209.

9 ( x + 1 ) ( x 2 + 3 ) 9 ( x + 1 ) ( x 2 + 3 )

211.

( 3 y + 5 ) ( 21 y 2 30 y + 25 ) ( 3 y + 5 ) ( 21 y 2 30 y + 25 )

213.

( 8 a 5 ) ( 8 a + 5 ) ( 8 a 5 ) ( 8 a + 5 )

215.

3 ( 3 q 1 ) ( 3 q + 1 ) 3 ( 3 q 1 ) ( 3 q + 1 )

217.

( 4 x 9 ) 2 ( 4 x 9 ) 2

219.

2 ( 4 p 2 + 1 ) 2 ( 4 p 2 + 1 )

221.

( 5 2 y ) ( 25 + 10 y + 4 y 2 ) ( 5 2 y ) ( 25 + 10 y + 4 y 2 )

223.

5 ( 3 n + 2 ) 2 5 ( 3 n + 2 ) 2

225.

( x 5 y ) ( x 5 + y ) ( x 5 y ) ( x 5 + y )

227.

( 3 x + 1 ) ( 3 x 2 + 1 ) ( 3 x + 1 ) ( 3 x 2 + 1 )

229.

Answers will vary.

231.

Answers will vary.

Section 6.4 Exercises

233.

( 2 n 1 ) ( n + 7 ) ( 2 n 1 ) ( n + 7 )

235.

a 3 ( a 2 + 9 ) a 3 ( a 2 + 9 )

237.

( 11 r s ) ( 11 r + s ) ( 11 r s ) ( 11 r + s )

239.

8 ( m 2 ) ( m + 2 ) 8 ( m 2 ) ( m + 2 )

241.

( 5 w 6 ) 2 ( 5 w 6 ) 2

243.

( m + 7 n ) 2 ( m + 7 n ) 2

245.

7 ( b + 3 ) ( b 2 ) 7 ( b + 3 ) ( b 2 )

247.

3 x y ( x 3 ) ( x 2 + 3 x + 9 ) 3 x y ( x 3 ) ( x 2 + 3 x + 9 )

249.

( k 2 ) ( k + 2 ) ( k 2 + 4 ) ( k 2 ) ( k + 2 ) ( k 2 + 4 )

251.

5 x y 2 ( x 2 + 4 ) ( x + 2 ) ( x 2 ) 5 x y 2 ( x 2 + 4 ) ( x + 2 ) ( x 2 )

253.

3 ( 5 p + 4 ) ( q 1 ) 3 ( 5 p + 4 ) ( q 1 )

255.

4 ( x + 3 ) ( x + 7 ) 4 ( x + 3 ) ( x + 7 )

257.

4 u 2 ( u + v ) ( u 2 u v + v 2 ) 4 u 2 ( u + v ) ( u 2 u v + v 2 )

259.

prime

261.

10 ( m 5 ) ( m + 5 ) ( m 2 + 25 ) 10 ( m 5 ) ( m + 5 ) ( m 2 + 25 )

263.

3 y ( 3 x + 2 ) ( 4 x 1 ) 3 y ( 3 x + 2 ) ( 4 x 1 )

265.

( 2 x 3 y ) ( 4 x 2 + 6 x y + 9 y 2 ) ( 2 x 3 y ) ( 4 x 2 + 6 x y + 9 y 2 )

267.

( y + 1 ) ( y 1 ) ( y 2 y + 1 ) ( y 2 + y + 1 ) ( y + 1 ) ( y 1 ) ( y 2 y + 1 ) ( y 2 + y + 1 )

269.

( 3 x y + 7 ) ( 3 x y 7 ) ( 3 x y + 7 ) ( 3 x y 7 )

271.

( 3 x 2 ) 2 ( 3 x 2 ) 2

273.

Answers will vary.

275.

Answers will vary.

Section 6.5 Exercises

277.

a = 10 / 3 , a = 7 / 2 a = 10 / 3 , a = 7 / 2

279.

m = 0 , m = 5 / 12 m = 0 , m = 5 / 12

281.

x = 1 / 2 x = 1 / 2

283.

a = −4 5 , a = 6 a = −4 5 , a = 6

285.

m = 5 / 4 , m = 3 m = 5 / 4 , m = 3

287.

a = −1 , a = 0 a = −1 , a = 0

289.

m = 12 / 7 , m = −12 / 7 m = 12 / 7 , m = −12 / 7

291.

y = −9 / 4 , y = 9 / 4 y = −9 / 4 , y = 9 / 4

293.

n = −6 / 11 , n = 6 / 11 n = −6 / 11 , n = 6 / 11

295.

x = 2 , x = −5 x = 2 , x = −5

297.

x = 3 / 2 , x = −1 x = 3 / 2 , x = −1

299.

x = 2 , x = −4 / 3 x = 2 , x = −4 / 3

301.

x = 3 / 2 x = 3 / 2

303.

x = 2 , x = −4 / 3 x = 2 , x = −4 / 3

305.

x = −3 / 2 , x = 1 / 3 x = −3 / 2 , x = 1 / 3

307.

p = 0 , p = ¾ p = 0 , p = ¾

309.

x = 0 , x = 6 x = 0 , x = 6

311.

x = 0 , x = –1 / 3 x = 0 , x = –1 / 3

313.

x=2x=2 or x=6x=6 (2,−4)(2,−4) (6,−4)(6,−4)

315.

x=32x=32 or x=34x=34
(32,−4)(32,−4) (34,−4)(34,−4)

317.

x=23x=23 or x=23x=23
(23,0)(23,0), (23,0)(23,0) (0,−4)(0,−4)

319.

x=53x=53 or x=12x=12
(53,0)(53,0), (12,0)(12,0) (0,−5)(0,−5)

321.

−13,−11−13,−11 and 11, 13

323.

−14,−12−14,−12 and 12, 14

325.

Width: 4 feet; Length: 7 feet.

327.

Width: 5 feet; Length: 11 feet.

329.

The sides are 6 feet and 8 feet.

331.

The building side is 8 feet, the hypotenuse is 17 feet, and the third side is 15 feet.

333.

0 seconds and 2 seconds 1 second

335.

Answers will vary.

Review Exercises

337.

3 a b 2 3 a b 2

339.

3 y 3 y

341.

7 ( 5 y + 12 ) 7 ( 5 y + 12 )

343.

3 x ( 6 x 2 5 ) 3 x ( 6 x 2 5 )

345.

4 x ( x 2 3 x + 4 ) 4 x ( x 2 3 x + 4 )

347.

−3 x ( x 2 9 x + 4 ) −3 x ( x 2 9 x + 4 )

349.

( a + b ) ( x y ) ( a + b ) ( x y )

351.

( x 3 ) ( x + 7 ) ( x 3 ) ( x + 7 )

353.

( m 2 + 1 ) ( m + 1 ) ( m 2 + 1 ) ( m + 1 )

355.

( a + 3 ) ( a + 11 ) ( a + 3 ) ( a + 11 )

357.

( m + 9 ) ( m 6 ) ( m + 9 ) ( m 6 )

359.

( x + 5 y ) ( x + 7 y ) ( x + 5 y ) ( x + 7 y )

361.

( a + 7 b ) ( a 3 b ) ( a + 7 b ) ( a 3 b )

363.

Prime

365.

3 y ( y 5 ) ( y 2 ) 3 y ( y 5 ) ( y 2 )

367.

( 5 y + 9 ) ( y + 1 ) ( 5 y + 9 ) ( y + 1 )

369.

( 5 y + 1 ) ( 2 y 11 ) ( 5 y + 1 ) ( 2 y 11 )

371.

−9 ( 9 a + 1 ) ( a 2 ) −9 ( 9 a + 1 ) ( a 2 )

373.

( 3 a 1 ) ( 6 a 1 ) ( 3 a 1 ) ( 6 a 1 )

375.

Prime

377.

3 ( x + 4 ) ( x 3 ) 3 ( x + 4 ) ( x 3 )

379.

3 ( 2 a 7 ) ( 3 a + 1 ) 3 ( 2 a 7 ) ( 3 a + 1 )

381.

( x 2 15 ) ( x 2 + 2 ) ( x 2 15 ) ( x 2 + 2 )

383.

( 5 x + 3 ) 2 ( 5 x + 3 ) 2

385.

10 ( 2 x + 9 ) 2 10 ( 2 x + 9 ) 2

387.

3 u 2 ( 5 u v ) 2 3 u 2 ( 5 u v ) 2

389.

( 13 m + n ) ( 13 m n ) ( 13 m + n ) ( 13 m n )

391.

( 3 + 11 y ) ( 3 11 y ) ( 3 + 11 y ) ( 3 11 y )

393.

n ( 13 n + 1 ) ( 13 n 1 ) n ( 13 n + 1 ) ( 13 n 1 )

395.

6 ( 4 p 2 + 9 ) 6 ( 4 p 2 + 9 )

397.

( 2 z 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 ) ( 2 z 1 ) ( 2 z + 1 ) ( 4 z 2 + 1 )

399.

( a + 3 3 b ) ( a + 3 + 3 b ) ( a + 3 3 b ) ( a + 3 + 3 b )

401.

( a 5 ) ( a 2 + 5 a + 25 ) ( a 5 ) ( a 2 + 5 a + 25 )

403.

2 ( m + 3 ) ( m 2 3 m + 9 ) 2 ( m + 3 ) ( m 2 3 m + 9 )

405.

4 x 2 ( 6 x + 11 ) 4 x 2 ( 6 x + 11 )

407.

( 4 n 7 m ) 2 ( 4 n 7 m ) 2

409.

5 u 2 ( u + 3 ) ( u 3 ) 5 u 2 ( u + 3 ) ( u 3 )

411.

prime

413.

( b 4 ) ( b 2 + 4 b + 16 ) ( b 4 ) ( b 2 + 4 b + 16 )

415.

( 2 b + 5 c ) ( b c ) ( 2 b + 5 c ) ( b c )

417.

5 ( q + 3 ) ( q 6 ) 5 ( q + 3 ) ( q 6 )

419.

10 ( m 5 ) ( m + 5 ) ( m 2 + 25 ) 10 ( m 5 ) ( m + 5 ) ( m 2 + 25 )

421.

( 4 x 3 y + 8 ) ( 4 x 3 y 8 ) ( 4 x 3 y + 8 ) ( 4 x 3 y 8 )

423.

b = −1 / 5 , b = −1 / 6 b = −1 / 5 , b = −1 / 6

425.

x = 1 / 2 x = 1 / 2

427.

x = −4 , x = −5 x = −4 , x = −5

429.

p = 5 2 , p = 8 p = 5 2 , p = 8

431.

m = 5 12 , m = 5 12 m = 5 12 , m = 5 12

433.

x = 2 , x = −5 x = 2 , x = −5

435.

p = 0 , p = ¾ p = 0 , p = ¾

437.

x=−7x=−7 or x=−4x=−4
(−7,−8)(−7,−8) (−4,−8)(−4,−8)

439.

x=78x=78 or x=78x=78
(78,0),(78,0), (78,0)(78,0) (0,−49)(0,−49)

441.

The numbers are −21−21 and −19−19 or 19 and 21.

443.

The lengths are 8, 15, and 17 ft.

Practice Test

445.

40 a 2 ( 2 + 3 a ) 40 a 2 ( 2 + 3 a )

447.

( x + 4 ) ( x + 9 ) ( x + 4 ) ( x + 9 )

449.

( x 8 ) ( y + 7 ) ( x 8 ) ( y + 7 )

451.

( 3 s 2 ) 2 ( 3 s 2 ) 2

453.

3 ( x + 5 y ) ( x 5 y ) 3 ( x + 5 y ) ( x 5 y )

455.

( x + 5 ) ( x 2 5 x + 25 ) ( x + 5 ) ( x 2 5 x + 25 )

457.

( 3 x 2 5 ) ( 2 x 2 3 ) ( 3 x 2 5 ) ( 2 x 2 3 )

459.

a = 4 / 5 , a = −6 a = 4 / 5 , a = −6

461.

The width is 12 inches and the length is 14 inches.

463.

x=3x=3 or x=4x=4 (3,−7)(3,−7) (4,−7)(4,−7)

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