Algebra II Honors
Chapter 4B
Name _________________
4.4 Factor each expression.
1. x2 + 11x + 28
2. x2 + 11x + 24
3. x2  7x  60
4. x2  10x + 21
5. x2 + 9x  18
6. x2  12x + 32
Factor each expression.
7. 5x2  17x + 6
8. 3x2 + 10x + 8
9. 2b2  9b  5
10. z2 + 12z + 36
11. 9x2  6x + 1
12. 4k2 + 12k + 9
Factor each expression completely.
13. 3x2 + 8x  3
14. 2x2  32x  128
15. 12t2 + 10t  12
16. 10x2 + x + 21
17. 4k2 + 2k + 30
18. x2  16x + 64
19. r2 – 144
20. 7s2 + 175
21. The area of a rectangular field is x2  x  72 m2. The length of the field is x + 8 m. What is the width of the
field in meters?
22. John is j years old. The product of his younger brother’s and older sister’s ages is j2  2j  15.
How old are John’s brother and sister in terms of John’s age?
4.5 Solve each equation by factoring. Check your answers.
23. x2 – 2x – 24 = 0
24. 3x2 = x + 4
25. x2 – 6x + 9 = 0
26. 3x2 + 45 = 24x
27. 4x2 + 6x = 0
28. 7x2 = 21x
29. (x + 2)2 = 49
30. x + 3 = 24x2
31. 25x2 + 20x + 4 = 0
32. 5x2 – 2x – 7 = 0
33. A woman drops a front door key to her husband from their apartment window several stories above the
ground. The function h = –16t2 + 64 gives the height h of the key in feet, t seconds after she releases it.
a. How long does it take the key to reach the ground?
b. What are the reasonable domain and range for the function h?
34. The function C = 75x + 2600 gives the cost, in dollars, for a small company to manufacture x items. The
function R = 225x – x2 gives the revenue, also in dollars, for selling x items. How many items should the
company produce so that the cost and revenue are equal?
Algebra II Honors
Chapter 4B
Name _________________
4.6 Solve each equation by finding square roots.
35. 3x2 = 75
36. 5x2  45 = 0
37. 4x2  49 = 0
38. 6x2 = 216
39. 2x2 = 14
40. 3x2  96 = 0
41. x2 + 22x +
42. x2  30x +
43. x2 + 5x +
1
44. x 2  x 
2
45. 25x2+ 10x +
46. 4x2 12x +
Complete the square.
Solve each quadratic equation by completing the square.
47. x2 + 10x  1 = 0
48. x2 + 2x  7 = 0
49. x2 + 6x + 10 = 0
50. x2 + 5x = 3x + 11
Rewrite each equation in vertex form.
51. y = x2  6x + 4
52. y = x2 + 14x + 50
53. y = 3x2 + 8x + 2
54. y = –2x2 + 6x  2
4.7 Solve each equation using the Quadratic Formula.
55. x2  8x + 15 = 0
56. x2 + 12x + 35 = 0
57. 3x2 + 5x = 2
58. 2x2 + 3 = 7x
59. x2 + 16 = 8x
60. x2 = 4x  1
61. x(2x  5) = 12
62. 3x2  8x + 16 = 0
63. x2 + 4x = 3
64. x2 + 10x + 22 = 0
Evaluate the discriminant for each equation. Determine the number of real solutions.
65. x2 + 5x + 8 = 0
66. x2  5x + 4 = 0
67. 9x2 + 12x  4 = 0
68. 3x2 + 5x  4 = 0
69. 4x2+ 4x = 1
70. 6x2 = x + 2
71. The equation y = x2  12x + 45 models the number of books y sold in a bookstore x days after an awardwinning author appeared at an autograph-signing reception. What was the first day that at least 100 copies
of the book were sold?
72. The height h, in feet, of a model rocket t seconds after launch is given by h = 256t  16t2. As the
rocket descends, it deploys a recovery parachute when it reaches 200 ft above the ground. At what
time does the parachute deploy?