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7. 6x2 + 29x − 5

8. 5 − l3b − 6b2

9. 6x2 + x − 35

10. −10x2 + 29x − 10

11. x2 − 16

12. x2 − 9

13. 4x2 − 1

14. 9x2 − 25

15. 49 − 9x2

16.(x + 3)(x + 2) = x2 + 5x + 6

17.(x − 7)(x − 2) = x2 − 9x + 14

18.(2a + 1)(a + 4) = 2a2 + 9a + 4

19.(3x − 2)(x − 5) = 3x2 − 17x + 10

20.(2t + 3)(3t − 5) = 6t2 − t − 15

6.8

1. 2a3 + 19a2 + 38a + 21

2. 6b3 + 13b2 + 16b + 15

3. 4c3 − 39c2 + 54c + 16

4. 8x4 − 18x3 + 17x2 − 19x + 7

5. y3 − y2 − 19y + 4

6. x3 − 6x2 + 12x − 8

7. t3 − 8

8. x3 + 1

9. x4 + 4x3 − 16x − 16

10. 2y4 − y3 − 8y2 + 34y − 15

6.9

1. 8c3d2

2. 5d4

3. 4x7

4. 5y4

5. −4x2 y

6. 1

7. −3t2

8. −18r2

9. 8x − 9x4

10. 5y3 − 7y5

11. x + 3

12. 9 − 13y

13. 8z8 − 7z7 + 6z6 − 5z5

14. 3x3y2 − 9x2y3 + 27xy4

15. 3x2 − x + 4

6.10

1. x − 7

2. y + 4

3. 2x + 3

4. 7x2 + 5

7. 2b − 1

9. x2 + 6

10. 4y2 − 2y + 1

7 Factoring

7.1

1. y(y − 15)

2. 3b(b − 2)

3. 8ab(4a + 5)

4. 5(y2 + 3y + 4)

5. x3y4(x5 − xy3 + y)

6. −a2(1 + a − 2a2)

7. 25x4(1 − 2x + 5x3)

8. 8r(r + 3t + 2)

9. 16x2 y(y − 3x)

10. 3xy(x + 2 + 5xy)

7.2

1.(x + 5)(x + 7)

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

3.(x − 3)(x − 5)

4.(x − 3)(x − 4)

5.(x + 5)(x − 4)

6.(x − 3)(x + 1)

7.(x − 9)(x − 2)

8.(x − 11)(x + 2)

9.(x + 13)(x − 3)

10.(x + 4)(x + 8)

7.3

1.(3x + 5)(x + 2)

2.(2x − 1)(x − 1)

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

4.(6x + 1)(2x + 5)

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

6.(10x + 1)(x − 5)

7.(3x − 5)(3x − 4)

8.(3x + 2)(6x + 1)

9.(3x + 1)(5x − 6)

10.(x − 6)(4x − 5)

7.4

1.(x + 7)(x − 7)

2.(x + 3)2

3.(6t + 1)(6t − 1)

4.(3t − 4)2

5.(4 + y)(4 − y)

6.(3y + 7)2

7.(2x + 9)(2x − 9)

8.(2x + 1)2

9.(4a + 3y)(4a − 3y)

10.(x − 6)2

8 Radicals

8.1

8.2

8.3

8.4

1. x = 9

2. No solution

3. x = 81

4. No solution

5. y = 50

6. No solution

7. x = 17

8. x = 26

9. x = 11

8.5

1. x = 5

2. x = 5

3. x = 4

4. x = −125

5. x = 3

7. x = 9

8. x = 25

9. x = −1.75

10. x = 11

8.6

9 Quadratic equations and their graphs

9.1

9.2

9.3

11. b2 − 4ac = 61, two irrational solutions

12. b2 − 4ac = −11, no real solutions

13. b2 − 4ac = 25, two rational solutions

14. b2 − 4ac = 0, one rational solution

15. b2 − 4ac = 24, two irrational solutions

16. b2 − 4ac = 1, two rational solutions

17. b2 − 4ac = 44, two irrational solutions

18. b2 − 4ac = −31, no real solutions

19. b2 − 4ac = 0, one rational solution

20. b2 − 4ac = 69, two irrational solutions

9.4

1. x = −2, x = −3

2. x = 4, x = 3

3. y = 2, y = −4

4. a = 5, a = −2

5. x = 4, x = −5

6. x = 5, x = 1

7. x = 0, x = −3

8. x = 0, x = 5

9.5

1.(3, 0),(1, 0),(0, 3)

2.(5, 0),(−1, 0),(0, −5)

3.(−2, 0),(0, 0)

4.(3, 0),(4, 0),(0, 12)

6. x = 4,(4, −1)

7. x = −2,(−2, −6)

8. x = 1,(1, 1)

9. x = 3,(3, 2)

10. x = 2,(2, 11)

9.6

10 Proportion and variation

10.1

1. 45°, 60°, 75°

2. 8 ft. and 12 ft.

3. 104 and 39

4. 20 oz

5. 24, 32, and 64

6. 20 and 24

7. 6 and 14

8. 51

9. 8 and 20

10. 6 and 20

10.2

1. x = 4.2

2. w = 15

3. x = 25

5. x = 15

6. x = 29

7. x = ±8

8. x = ±5

9. x = ±13

10. x = 7, x = −4

10.3

1. 42

2. 100

3. 312

4. 1275

5. 700

6. 0.009 V

7. 143 mi

8. 0.6 mi

9. 304 cm3

10. 70 mi

10.4

1. y = 3

2. x = 16

3. y = 8

4. t = 44

5. a = 12

6. 4 cm

7. 14.4 psi

8. 5.5 h

9. Approximately 2.8 × 1012 N

10. 3 ft

10.5

1. y = 180

2. x = 8

3. z = 7

4. y = 5

5. x = 21

6. z = 42

7. 20 cm

8. Approximately 683 N

9. Approximately 7.8 ft3

11 Rational equations and their graphs

11.1

11.2

11.3

11.4

11.5

11.6

11.7

6. y = −5

7. x = 3

8. x = 8

9. x = −9

10. x = 4

11.8

11.9

2. 2.4 min

3. 9 h

6. 3 mon

7. 2.1 days

9. 18 h

12 Exponential growth and decay

12.1

1. $5304.50

2. $14802.44

3. $2977.73

4. $3052.24

5. $327,148.96

6. $6204.59

7. $8492.03

8. $5977.69

9. $30,491.91

10. $59,913.95

12.2

1. Growth

2. Decay

3. Decay

4. Growth

5. Decay

6. Growth, 3,355,443,200 bacteria

7. Decay, 102.4 mg

8. Growth, approximately 379,518

9. Decay, $16,355.33

10. Decay, 36,652.78 acres

12.3

13 Matrix algebra

13.1

1. 2 × 4

2. 1 × 4

3. 3 × 2

4. 2 × 1

5. 3 × 3

6. b(1, 3)