Practice 10-1 Write each polynomial in standard form. Then name each polynomial by its degree and the number of its terms. 1. 4y 3 4y 2 3 y 2. x 2 x 4 6 3. x 2 4. 2m 2 7m 3 3m 5. 4 x 2x 2 6. 7x 3 2x 2 7. n 2 5n 8. 6 7x 2 9. 3a 2 a 3 4a 3 10. 5 3x 11. 7 8a 2 6a 12. 5x 4 x 2 13. 2 4x 2 x 3 14. 4x 3 2x 2 15. y 2 7 3y 16. x 6x 2 3 17. v 3 v 2v 2 18. 8d 3d 2 Find each sum or difference. Write your answer in standard form. 19. (3x 2 5x) (x 2 4x 3) 20. (2x 3 4x 2 3) (x 3 3x 2 1) 21. (3y 3 11y 3) (5y 3 y 2 2) 22. (3x 2 2x 3 ) (3x 2 7x 1) 23. (2a 3 3a 2 7a) (a 3 a 2 2a) 24. (8y 3 y 7) (6y 3 3y 3) 25. (x 2 6) (5x 2 x 3) 26. (5n 2 7) (2n 2 n 3) 27. (5n 3 2n 2 2) (n 3 3n 2 2) 28. (3y 2 7y 3) (5y 3 4y 2 ) 29. (2x 2 9x 17) (x 2 6x 3) 30. (3 x 3 5x 2 ) (x 2x 3 3) 31. (3x x 2 x 3 ) (x 3 2x 2 5x) 32. (d 2 8 5d) (5d 2 d 2d 3 3) 33. (3x 3 7x 2 ) (x 2 2x 3 ) 34. (6c 2 5c 3) (3c 2 8c) 35. (3y 2 5y 7) (y 2 6y 7) 36. (3c 2 8c 4) (7 c 2 8c) 37. (4x 2 13x 9) (12x 2 x 6) 38. (2x 13x 2 3) (2x 2 8x) 39. (7x 4x 2 11) (7x 2 5) 40. (4x 7x 3 9x 2 ) (3 2x 2 5x) 41. (y 3 y 2 2) (y 6y 2 ) 42. (x 2 8x 3) (x 3 8x 2 8) 43. (3x 2 2x 9) (x 2 x 7) 44. (2x 2 6x 3) (2x 4x 2 2) 45. (2x 2 2x 3 7) (9x 2 2 x) 46. (3a 2 a 3 1) (2a 2 3a 1) 47. (2x 2 3 x) (2 2x 2 5x) 48. (n 4 2n 1) (5n n 4 5) 49. (x 3 3x) (x 2 6 4x) 50. (7s 2 4s 2) (3s 2 s 2 ) 51. (6x 2 3x 9) (x 2 3x 5) 52. (3x 3 x 2 4) (2x 3 3x 9) 53. (y 3 3y 1) (y 3 3y 5) 54. (3 5x 3 2x) (x 2x 2 4x 3 ) 55. (x 2 15x 13) (3x 2 15x 7) 56. (7 8x 2 ) (x 3 x 5) 57. (2x 3) (x 4) (x 2) 58. (x 2 4) (x 4) (x 2 2x) 18 Adding and Subtracting Polynomials Algebra Chapter 10
Practice 10-2 Find each product. 1. 4(a 3) 2. 5(x 2) 3. 3x 2 (x 2 3x) 4. 4x 3 (x 3) 5. 5x 2 (x 2 2x 1) 6. 3x(x 2 5x 3) 7. x 2 ( 2x 2 3x 2) 8. 4d 2 (d 2 3d 7) 9. 5m 3 (m 6) 10. a 2 (2a 4) 11. 4(x 2 3) x(x 1) 12. 4x(5x 6) Find the greatest common factor (GCF) for each polynomial. 13. 8x 4 14. 15x 45x 2 15. x 2 3x 16. 4c 3 8c 2 8 17. 12x 36 18. 12n 3 4n 2 19. 14x 3 7x 2 20. 8x 3 12x 21. 9 27x 3 22. 25x 3 15x 2 23. 11x 2 33x 24. 4n 4 6n 3 8n 2 25. 8d 3 4d 2 12d 26. 6x 2 12x 21 27. 8g 2 16g 8 Factor each expression. 28. 8x 10 29. 12n 3 8n 30. 14d 2 31. 6h 2 8h 32. 3z 4 15z 3 9z 2 33. 3y 3 8y 2 9y 34. x 3 5x 2 35. 8x 3 12x 2 4x 36. 7x 3 21x 4 37. 6a 3 12a 2 14a 38. 6x 4 12x 2 39. 3n 4 6n 2 9n 40. 2w 3 6w 2 4w 41. 12c 3 30c 2 42. 2x 2 8x 14 43. 4x 3 12x 2 16x 44. 16m 3 8m 2 12m 45. 4a 3 20a 2 8a 46. 18c 4 9c 2 7c 47. 6y 4 9y 3 27y 2 48. 6c 2 3c 49. A circular pond will be placed on a square piece of land. The length of a side of the square is 2x. The radius of the pond is x. The part of the square not covered by the pond will be planted with flowers. What is the area of the square that will be planted with flowers? 50. A square poster of length 3x is to have a square painting centered on it. The length of the painting is 2x. The area of the poster not covered by the painting will be painted black. a. What is the area of the poster that will be painted black? b. Find the area when x 12 in. 51. The formula for the surface area of a sphere is A 4πr 2. A square sticker of side x is placed on a ball of radius x. a. What is the area of the sphere not covered by the sticker? b. Find the area not covered when x 5 in. 20 Multiplying and Factoring Algebra Chapter 10
Practice 10-3 Find each product. 1. (x 3)(2x 5) 2. (x 2 x 1)(x 1) 3. (3w 4)(2w 1) 4. (x 5)(x 4) 5. (2b 1)(b2 3b 4) 6. (a 11)(a 5) 7. (2g 3)(2g 2 g 4) 8. (3s 4)(s 5) 9. (4x 3)(x 7) 10. (x 6)(x 2 4x 3) 11. (5x 3)(4x 2) 12. (3y 7)(4y 5) 13. (3x 7)(x 5) 14. (5x 2)(x 3) 15. (3m 2 7m 8)(m 2) 16. (a 6)(a 8) 17. (x 2)(2x 2 3x 2) 18. (a 2 a 1)(a 1) 19. (x 2)(x 2 4x 4) 20. (2r 1)(3r 1) 21. (k 4)(3k 4) 22. (2n 3)(n 2 2n 5) 23. (p 4)(2p 3) 24. (3x 1)(4x 2 2x 1) 25. (2x 2 5x 2)(4x 3) 26. (x 7)(x 5) 27. (6x 11)(x 2) 28. (2x 1)(4x 3) 29. (3x 4)(3x 4) 30. (6x 5)(3x 1) 31. (n 7)(n 4) 32. (3x 1)(2x 1) 33. (d 9)(d 11) 34. (2x 2 5x 3)(2x 1) 35. (b 8)(2b 5) 36. (2x 5)(x 4) 37. (3x 5)(5x 7) 38. (x 5)(2x 2 7x 2) 39. (2x 2 9x 11)(2x 1) 40. (2x 2 5x 4)(2x 7) 41. (x 2 6x 11)(3x 5) 42. (5x 7)(7x 3) 43. (4x 7)(2x 5) 44. (x 9)(3x 5) 45. (2x 1)(x 2 7x 1) 46. The width of a rectangular painting is 3 in. more than twice the height. A frame that is 2.5 in. wide goes around the painting. a. Write an expression for the area of the painting and frame. b. Find the area when the height of the painting is 12 in. c. Find the area when the height of the painting is 15 in. 47. The Robertsons put a rectangular pool in their backyard with a stone walkway around it. The total length of the pool and walkway is 3 times the total width. The walkway is 2 ft wide. a. Write an expression for the area of the pool. b. Find the area of the pool when the total width is 10 ft. c. Find the area of the pool when the total width is 9 ft. 48. Suppose you deposit $1500 in a savings account that has an annual interest rate r. At the end of 3 yr the amount of money in your account would be 1500(1 2r r 2 )(1 r). a. Simplify the expression and write your answer in standard form. b. Find the amount of money in the account at the end of three years if the interest rate is 4%. c. Find the amount of money in the account at the end of 3 yr if the interest rate is 6%. 22 Multiplying Polynomials Algebra Chapter 10
Practice 10-4 Use tiles to factor each expression. 1. 2x 2 3x 1 2. d 2 8d 7 3. y 2 6y 8 4. b 2 2b 3 5. s 2 4s 5 6. 2a 2 5a 3 7. 2n 2 n 6 8. 3x 2 x 4 9. a 2 3a 2 10. p 2 8p 7 11. d 2 6d 5 12. n 2 n 6 Factor each expression. 13. x 2 5x 14 14. b 2 9b 14 15. 2y 2 9y 5 16. a 2 7a 12 17. 5x 2 2x 7 18. 7n 2 9n 2 19. x 2 8x 12 20. x 2 7x 18 21. n 2 7n 10 22. s 2 5s 14 23. x 2 9x 8 24. x 2 2x 24 25. 3c 2 17c 6 26. 3x 2 8x 4 27. x 2 7x 10 28. 6x 2 7x 10 29. m 2 4m 21 30. 3x 2 10x 8 31. x 2 5x 24 32. b 2 4b 60 33. 3a 2 16a 12 34. m 2 7m 10 35. n 2 n 72 36. k 2 6k 5 37. 5x 2 2x 3 38. 3a 2 7a 2 39. 3b 2 7b 2 40. d 2 4d 3 41. b 2 26b 48 42. n 2 15n 26 43. n 2 n 6 44. z 2 14z 49 45. 7r 2 10r 3 46. 3x 2 8x 5 47. 2b 2 9b 4 48. t 2 6t 27 49. b 2 4b 12 50. d 2 11d 18 51. 5x 2 7x 2 52. x 2 13x 42 53. 5x 2 22x 8 54. 4n 2 17n 15 55. 3a 2 5a 2 56. h 2 7h 18 57. x 2 3x 10 58. p 2 12p 28 59. y 2 6y 55 60. b 2 3b 4 61. 5a 2 33a 14 62. 3b 2 2b 8 63. 3x 2 7x 6 64. r 2 2r 35 65. c 2 3c 10 66. x 2 8x 15 67. 2x 2 13x 24 68. n 2 23n 60 69. c 2 3c 10 70. 4r 2 11r 3 71. 2m 2 9m 7 72. 5x 2 3x 2 73. y 2 16y 64 74. n 2 10n 25 75. r 2 14r 51 76. 7a 2 19a 10 77. x 2 x 42 78. n 2 2n 63 79. a 2 7a 6 80. 7a 2 30a 8 81. 3m 2 17m 10 82. n 2 16n 36 83. n 2 4n 21 84. y 2 16y 17 24 Factoring Trinomials Algebra Chapter 10
Practice 10-5 Factor each expression. 1. x 2 9 2. 4m 2 1 3. a 2 2a 1 4. 4x 2 12x 9 5. x 2 22x 121 6. n 2 4 7. 9x 2 4 8. 16c 2 49 9. 9x 2 30x 25 10. 4x 2 20x 25 11. 2a 2 18 12. x 2 24x 144 13. 3n 2 3 14. 9h 2 60h 100 15. 9d 2 49 16. 81a 2 400 17. r 2 36 18. 3a 2 48 19. b 2 4b 4 20. 10x 2 90 21. 25x 2 64 22. 12w 2 27 23. g 3 25g 24. x 2 6x 9 25. a 2 25 26. 36s 2 225 27. 4b 2 44b 121 28. x 2 16x 64 29. x 2 2x 1 30. d 2 49 31. x 3 36x 32. 9y 2 289 33. x 2 30x 225 34. 100a 2 9 35. 2x 2 4x 2 36. 5n 3 20n 37. 9n 2 12n 4 38. d 2 169 39. 4a 2 81 40. x 2 121 41. 5x 2 40x 80 42. 16n 2 56n 49 43. 3n 2 30n 75 44. a 2 26a 169 45. 25x 2 144 46. 9d 2 64 47. n 2 28n 196 48. 49a 2 14a 1 49. y 2 8y 16 50. y 2 400 51. x 2 10x 25 52. 4x 2 60x 225 53. 3x 2 363 54. y 2 81 55. a 2 100 56. 256a 2 1 57. n 2 34n 289 58. 2d 3 50d 59. y 2 22y 121 60. 144x 2 25 61. 4x 2 169 62. x 2 12x 36 63. 64r 2 80r 25 64. 50m 3 32m 65. b 2 225 66. x 2 18x 81 67. b 2 64 68. 16x 2 72x 81 69. b 2 256 70. x 2 24x 144 71. 225x 2 16 72. 2x 3 40x 2 200x 73. 4r 2 25 74. 16x 2 8x 1 75. b 2 14b 49 76. x 2 30x 225 77. m 2 28m 196 78. 9r 2 256 79. b 2 20b 100 80. m 2 16 81. 4x 2 32x 64 82. x 2 196 83. 8x 3 32x 84. 25x 2 30x 9 85. 8m 2 16m 8 86. 9x 2 400 87. m 2 144 26 Factoring Special Cases Algebra Chapter 10
Practice 10-6 Solve each equation. 1. (x 9)(x 8) 0 2. x 2 9x 10 0 3. (c 21)(c 21) 0 4. (x 12)(5x 13) 0 5. 2a 2 21a 65 0 6. (x 7)(x 13) 0 7. a 2 6a 72 0 8. (2x 3)(2x 7) 0 9. (4d 10)(5d 8) 0 10. (n 12)(n 8) 0 11. 2s 2 13s 24 0 12. x 2 5x 150 13. 3c 2 8c 3 14. (6a 1)(5a 21) 0 15. (c 9)(c 9) 0 16. (x 18)(x 17) 0 17. x 2 121 18. x 2 21x 108 0 19. 2d 2 3d 54 20. (5n 16)(n 11) 0 21. (n 13)(n 27) 0 22. (x 8)(x 15) 0 23. x 2 35x 300 0 24. 9x 2 4 0 25. Suppose you are building a storage box of volume 4368 in. 3. The box will be 24 in. long. The height of the box will be 1 in. more than its width. Find the height and width of the box. 26. A banner is in the shape of a right triangle of area 63 in. 2. The height of the banner is 4 in. less than twice the width of the banner. Find the height and width of the banner. 27. A rectangular poster has an area of 190 in. 2. The height of the poster is 1 in. less than twice its width. Find the dimensions of the poster. 28. A diver is standing on a platform 24 ft above the pool. He jumps from the platform with an initial upward velocity of 8 ft/s. Use the formula h 16t 2 vt s, where h is his height above the water, t is time, v is his starting upward velocity, and s is his starting height. How long will it take for him to hit the water? Simplify each equation and write in standard form. Then solve the equation. 29. (x 11)(x 10) 0 30. m 2 169 0 31. 2m 2 5m 42 32. m 2 8m 9 33. (2t 5)(2t 1) 0 34. (b 17)(b 21) 0 35. (3y 1)(y 6) 0 36. 2x 2 50 25x 37. (x 6)(x 7) 0 38. x 2 26x 168 0 39. m 2 13m 30 40. (x 14)(x 3) 0 41. 4x 2 2x 2 42. x 2 13x 42 43. 3t 2 75 44. (2b 7)(2b 13) 0 45. (4t 5)(t 8) 0 46. 3x 2 5x 2 0 47. t 2 23t 132 48. 5b 2 37b 130 0 49. 2b 2 b 28 50. (x 8)(5x 3) 0 51. 3x 2 21x 54 52. 2x 2 512 53. y 2 8y 65 54. (y 2)(5y 9) 0 55. (y 4)(5y 8) 0 28 Solving Equations by Factoring Algebra Chapter 10
Practice 10-7 Solve each quadratic equation by any method. If the equation has no real solutions write no real solutions. Round your answers to the nearest hundredth. 1. x 2 8x 5 0 2. x 2 36 0 3. d 2 4d 96 0 4. a 2 3a 154 0 5. 4p 2 12p 91 0 6. 5m 2 9m 126 7. r 2 35r 70 0 8. y 2 6y 247 0 9. x 2 12x 40 0 10. 4n 2 81 0 11. x 2 13x 30 0 12. a 2 a 132 13. 6w 2 23w 7 0 14. 4x 2 33x 27 15. 7s 2 7 0 16. x 2 5x 90 0 17. 5b 2 20 0 18. 4x 2 3x 6 0 19. 6h 2 77h 13 0 20. 5y 2 17y 12 21. g 2 15g 54 22. 27f 2 12 23. 4x 2 52x 133 0 24. x 2 36x 60 0 25. a 2 2a 360 0 26. x 2 10x 40 0 27. t 2 10t 39 28. 4x 2 7x 9 0 29. 2c 2 39c 135 0 30. 4x 2 33x 340 0 31. m 2 40m 100 0 32. 8x 2 25x 19 0 33. 36w 2 289 0 34. 4d 2 29d 60 0 35. 4z 2 43z 108 0 36. 3x 2 19x 40 0 37. 14x 2 56 38. 32x 2 18 0 39. r 2 r 650 0 40. 2y 2 39y 17 41. 5a 2 9a 5 0 42. x 2 9x 120 43. 8h 2 38h 9 0 44. 20x 2 245 45. 9h 2 72h 119 46. x 2 3x 8 0 47. 6m 2 13m 19 48. 9x 2 81 0 49. 4s 2 8s 221 50. 6p 2 25p 119 0 51. 2s 2 59s 17 0 52. A rectangular painting has dimensions x and x 10. The picture is in a frame 2 in. wide. The total area of the picture and frame is 900 in. 2. What are the dimensions of the painting? 53. A ball is thrown upward from a height of 15 ft with an initial upward velocity of 5 ft/s. Use the formula h 16t 2 vt s to find how long it will take for the ball to hit the ground. 54. Your community wants to put a square fountain in a park. Around the fountain will be a sidewalk that is 3.5 ft wide. The total area that the fountain and sidewalk can be is 700 ft 2. What are the dimensions of the fountain? 55. The Garys have a triangular pennant of area 420 in. 2 flying from the flag pole in their yard. The height of the triangle is 10 in. less than 5 times the base of the triangle. What are the dimensions of the pennant? 30 Choosing an Appropriate Method for Solving Algebra Chapter 10