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10.1 Factoring Common Monomials

1. 15

2. 3

3. 8x

4. relatively prime

5. x2y2 6. 2ab

7. 3(x + y)

8. a(x + y)

9. 8(x – 4y)

10. 15(x + 2)

12. 10(–5x + 1)

13. prime

14. x(x – 3)

15. 7(x2 – 7xy + 4y2) 16. 3(7x3 – 2x2 – 1) 17. 6(a2 + 8a – 4) 18. prime

19. 3ab(2a + b)

Section 10.1 23. prime

24. 2π_{(–2r + x)}

25. 4x(3x2 – 4y2)

26. 10x(2a3 + 5a + 1) 27. 14x(4x + 3y – 2)

28. prime

29. 7a(a4 – 12a2 + 3) 30. x(x4 + x2 – x + 1) 31. (x – 2)(x + 8)

32. (2y – 1)(4y – 3)

33. (b + c)(5 + a)

34. (y – z)(6x – 7)

35. 42 in.2 = 1 in. × _{42 in. = 2} in. × _{21 in. = 3 in.} × _{16 in. =} 6 in. × _{7 in.}

36. 12 children; 9 rows

37. 13 cookies

38. 3x – 1

39. 2π_{(x + y); x + y}

40. 3x2y4z3(2x2y – 9xy2z + 6z2) 41. 17a2b5(2a5b3c2 + 3ad4 –

y

(2, 4) (4, 2) (₂1, 3)

(₂3, 1)

44. 1 km

45a. 555.6 m

45b. 1822 ft

45c. 405.6 m; 1330 ft

46. D = {–3, –1, 2, 4}

47. R = {1, 2, 3, 4}

48. yes

49. {(–3, 1), (–1, 3), (2, 4), (4, 2)}

50.

51. x2 – 3x – 40 52. x2 – 13x + 40 53. x2 + 3x – 40 54. 3x2 + 15x – 42

10.2 Factoring Trinomials of the Form x2 ₊ bx ₊ c

1. (a + 3)(a + 5)

2. (x + 6)(x + 9)

3. (a – 3)(a – 1)

4. (x + 8)(x – 4)

5. (b + 5)(b – 4)

6. (x + 1)(x – 3)

7. (a + 4)(a – 2)

8. (a + 7)(a – 4)

9. prime

10. prime

11. (x – 5)(x – 4)

12. (x – 10)(x – 1)

13. (y + 5)(y + 2)

14. prime

15. prime

16. (a – 15)(a + 2)

17. (x + 10y)2 18. (x + 3y)2

19. (x – 2y)(x – 48y)

20. (x – 3y)(x – 15y)

21. (a – 18b)(a + 4b)

23. (x + 4)(x + 14)

24. (y – 2)(y – 24)

25. (x – 3)(x + 18)

26. 6(b – 4)(b – 3)

27. 3(x – 9)(x + 1)

28. a(x – 12)(x + 1)

29. 3(x + 6)(x + 2)

30. 4(x – 8)(x – 3)

31. x2(x + 8)(x – 2)

32. (x – 4)(x – 14); 10 units

33. x2 + 32x + 60; (x + 30)(x + 2)

34. –ax(x + 3)(x – 48)

35. 4a2b(a + 2b)(a – 5b) 36. b(x2 – 24)(x2 + 5) 37.

Section 10.2 38b.

39.

40. y ≈ _{–0.5x + 978.3}

41. trinomial

42. 8

43. 6

44. 7

45. x2y3(6x – 27yz + 8) 46. 6x2 + 29x + 35

10.3 Factoring Trinomials of the Form ax2 ₊ bx ₊ c

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

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

3. (x – 4)(3x – 2)

4. (3x – 5)2

5. (3x – 7)(x + 4)

6. (x – 3)(2x + 7)

7. (3x + 4)(2x – 1)

8. (3b + 2)(2b – 5)

9. (3c + 2)(5c + 3)

10. (3x + 2)(4x + 3)

11. (2a + 1)(3a – 4)

12. (3x – 1)(3x + 2)

13. (5x + 1)(x – 3)

14. (2x – 1)(x + 7)

15. (x + 3y)(5x – 7y)

16. (6x + 5y)(x – 4y)

17. 3(x – 2)(2x + 5)

18. 10(3x + 5)(x – 5)

19. 8(2a – b)(a + 3b)

20. 4(x + y)(3x – 5y)

21. (m – 5n)(m + 4n)

2

2

2 2

3x

5x

23. (x – 2y)(x + 5y)

24. (x + 7y)(x – 14y)

25. 2(x – 8)(x + 4)

26. 8(a + 1)(a – 14)

27. 3ab(b – 1)(4b + 7)

28. 17xy(x + 1)(3x – 5)

29. 3(5x + 3)(3x – 2)

30. 2(7x + 4)(2x – 3)

31. 2(x + 4y)(x – 13y)

32. 3(x – 11y)(x + 14y)

33. 6(8x – 3)(3x – 1)

34. a2b(a + 2)(3a – 5)

35. (5x + 4)(3x + 4)

36.

37. 5 : 3

Section 10.3

y

x

39. using the polynomial: 4(5)2 + 104(5) + 651

= 100 + 520 + 651 = 1271

using the factored form: [2(5) + 21][2(5) + 31] = (10 + 21)(10 + 31) = 31(41) = 1271

40. 304 ft2 41. 25x2 – 9 42. x = 9

43. (6, 2)

44. 2x2 + 4x + 9 45. 3x – 4

46. 5x + 2

47. x < ₅

48.

49. 20 hr

10.4 Special Patterns

1. +, – or –, +

2. +, – or –, +

3. 2, 2

4. 10, 10

5. 6a, 7

6. 7, 5x

7. yes; 3x doubled = 6x

8. yes; 7x doubled = 14x

9. no; x2y is not a perfect square

11. no; 2x(5) doubled = 20x

12. no; – 4b2 is not a perfect square

13. (a – 15b)(a + 15b)

14. (ax – y)(ax + y)

15. (x – 3)2 16. (4a + 1)2 17. (x – 8)2 18. (m + 12)2 19. (a – 5b)2

Section 10.4 21. 2(a – 11)(a + 11)

22. 3(x – 7)(x + 7)

23. (3x + 2)2 24. (6x + 1)2

25. x2(a – 4)(a + 4) 26. a2(a – b)(a + b) 27. (3x + 5z)2

28. prime

29. 4(2x – 1)(2x + 1)

30. x5(x – 1)(x + 1) 31. prime

32. (x + 0.3)2

33. 7(3x – 5)(3x + 5)

34. 3(7a – 13)(7a + 13)

35. 18b4c(3a – 1)(3a + 1) 36. x2(x2 + 1)(x + 1)(x – 1) 37. 3xy(3x2 – 4y)2

38. (3x + 8)2;

2

9 48 64

3 8

3 8

x x

x x

+ +

= + +

39. 17,952 days ≈ _{49 yr}

41a. y ≈ _–3.66x2 _{+ 30.86x} + 196.34

41b.

42. Friction between the side walls of the valley and the edges of the glacier causes the edges to move slower. Thicker ice in the center of the glacier allows for a

faster flow at the top of the glacier. The Internet

keyword search glacial

processes will provide some interesting information and diagrams.

43. –15

44. –3x + 6

Section 10.4

y

x

46.

47. –2323

48. 73 × ₁₀₁

49. 2323

23 −

= –101 or

2323 101 −

− = 23;

7373

73 = 101 or 7373

101 = 73

50. 2(x + 2);

(2x + 4) ÷ _{2 = (x + 2) or} (2x + 4) ÷ _{(x + 2) = 2}

51. –5x(8y2 – y – 4);

2

40 5 20

5

xy xy x x

− + +

− =

8y2 – y – 4 or

2

2

40 5 20

8 4

xy xy x y y

− + +

− − = –5x

52. (x – 1)(x + 9);

2 8 9 9 x x x + −

+ = x – 1 or

2 8 9 1 x x x + −

10.5 Factoring Completely

1. 5(a + 1)2 2. x(x – 1)2

3. 2(10 – a)(10 + a)

4. 2a6(2a – 1)(2a + 1) 5. 3(x – 2)(x – 4)

6. a3(3a2 – 4) 7. 5(x – 7)2 8. (m5 + 1)2

9. (x + y)(2x – y)

10. (4 – m)(b + c)

12. (x + 2)(t – 3w)

13. (a + b – 2)(m + n)

14. (m + n)(2a + b)

15. 8(a – 3b2)2

16. 3x(x – 4)(x – 7)

17. (x2 + 4)(x – 2)(x + 2)

18. (a2x2 + 9)(ax + 3)(ax – 3) 19. 3(3x + 4)(2x – 3)

20. 5(3y + 4)(2y – 5)

Section 10.5 23. (w + x)(y + z)

24. (x + 3)(y + 5)

25. (x + 7)(y – 6)

26. (x – 3y)(x – 2)

27. (x + 4)(6x + y2)

28. (x – y)(x + y)(2a + b)

29. (y – 2)(y + 2)(y – 3)

30. (a – 3)(a + 3)(a + 2)

31. 5(y – 1)(y + 1)(y – 3)

32. 3(x – 4)(x + 4)(x – 2)

33. (x – 2)(x + 3)(x – 4)

34. (x + 2)2(x – 3)

35. (y + 1)(y – 3)(2y – 5)

36. (y + 4)(y + 2)(3x – 1)

37. (x + y – 3)(x + y + 3)

38. [(x + y) + 1]2 or (x + y + 1)2 39a. 10,496 ft

39b. ≈ _2.3 × ₁₀6 _ft3

40a. ≈ _{0.44 = 44% grade}

40b. ≈ _{0.20 = 20% grade}

41a. 0.8 km/min

41b. 30 mi/hr

43. q 7n 5 A

+ =

44. 24

11

m q =

45. 7

5

q

x

= +

46. 11 quarters, 13 dimes, and 7 nickels

47. 21 quarters, 14 dimes, and 7 nickels

48. plane: 183 mi/hr; wind: 8 mi/hr

49. current: 0.5 mi/hr; boys: 4.5 mi/hr

50. 1.875 gal of the 40%

solution and 1.125 gal of water

Chapter 10 Review

1. r(3r + 5)

2. 2x(4xy3 + 3y2 – 1) 3. 4x2(x – 2)

4. x2(x2 + 3xy + 7) 5. (y – 7)(y – 8)

6. (x + 9)(x – 6)

7. (2d + 7)(d + 1)

8. (3t – 1)(3t + 8)

9. (x + 7)(x – 2)

10. (a + 7)(a – 12)

11. (5b + 3)(3b – 2)

12. (2y + 1)(y + 7)

13. (a – 3)(a + 3)

14. (5x – 12y)(5x + 12y)

15. (a + 7)2 16. (3x – 5)2

17. y(x + 8)(x – 7)

18. 7(y – 2)(y – 1)

19. 2(9x – 5)(x – 5)

20. 4(3x – 5)(x – 4)

21. 2(x – 9)(x – 6)

23. prime

24. x(9x – 25)

25. 2(3y – 5)(3y + 5)

26. prime

27. 24(x – 2y)(x + 2y)

28. 5(b – 5)2 29. (3b – 2c)2

30. (2a – 3)(a + 6)

31. (3x – y)(5x + 2y)

32. (3y + 5)(y + 4)

33. prime

34. 6(2x + 3y)(x + 5y)

35. 2(3a – 7)(a – 1)

36. prime

37. 2(3y – 5)(2y + 7)

38. (9r + 2s)(r + 1)

39. (2x2 – 3)(5x + 7) 40. (x2 + 3)2

41. (c2 + 2)(c2 + 1)

42. (x + y – 3)(x + y + 3)

Chapter 10 Review 46. S = π_{r(l + r)}

47. x2 + xy + y2

48. (2w + 7)(2w + 5)

49. 35 in.2 50a. 99 in.2

Sequences—Factorial Sequences

1. 3 × ₂ × _{1 = 6}

2. 6 × ₅ × ₄ × ₃ × ₂ × _{1 = 720}

3. 8!

4. 5!

5. 2.667, 2.708, 2.717

6. 2.71806, 2.71825, 2.71828

7. 2.7182815, 2.7182818, 2.7182818