1. Which is the correct factorization of $x^2 - 6x + 8$?
2. The polynomial $p(x) = x^3 - 4x^2 - 7x + 10$ has $(x - 1)$ as a factor. What are all the other zeros of $p(x)$?
3. Which of the following is equivalent to $(5x^2 - 3x + 7) - (2x^2 + 4x - 1)$?
4. What is the value of $f(3)$ for $f(x) = x^2 - 4x + 4$?
5. What is $(x - 1)(x + 4)$?
6. Factor: $x^2 - 9$
7. What are the solutions to the quadratic equation $x^2 - 4x + 4 = 0$?
8. What is the value of $f(0)$ for $f(x) = 3x^2 - 4x + 7$?
9. A polynomial used in a calculation is $x^2-6x+9$. Factor: $x^2-6x+9$.
10. A revenue expression is $x^2+x-12$. Factor: $x^2+x-12$.
11. Factor: $x^2 - 10x + 21$
12. Which of the following lists all the solutions to the quadratic equation $2x^2 - 5x - 12 = 0$?
13. What is the value of $f(0)$ for $f(x) = x^2 - 2x + 1$?
14. The polynomial $P(x) = x^3 - 2x^2 - 5x + 6$ has $(x - 1)$ as a factor. What are the other two roots of $P(x) = 0$?
15. A rectangular garden has a length that is 3 feet longer than its width. If the perimeter of the garden is 54 feet, what is the area of the garden, in square feet?
16. What is the value of the expression $2x^3 - x^2 + 3x + 5$ when $x = -2$?
17. Which of the following expressions is equivalent to $(2x - 3)^2$?
18. Which of the following expressions is equivalent to $x^2 + 2x - 24$?
19. What is the sum of all real solutions to the rational equation $\dfrac{x^2 - x}{x - 3} = \dfrac{6}{x - 3}$?
20. If the polynomial $P(x) = x^3 - 3x^2 + kx + 10$ is divisible by $(x - 2)$ without a remainder, what is the value of the constant $k$?
21. Solve: $x^2 + 4x - 21 = 0$
22. Which is the correct factorization of $x^2 + 6x + 9$?
23. Factor: $x^2 + 8x + 16$
24. Which is the correct factorization of $x^2 - 4x - 12$?
25. What are the solutions to the quadratic equation $x^2 - 3x - 10 = 0$?
26. What are the solutions to the quadratic equation $x^2 - 2x - 8 = 0$?
27. Factor: $x^2 + 2x - 15$
28. What is the value of $f(-1)$ for $f(x) = x^2 + 2x - 3$?
29. Which is the correct factorization of $x^2 + x - 12$?
30. Factor: $x^2 + 3x - 18$
31. What is the value of $f(2)$ for $f(x) = x^2 - 3x + 2$?
32. What is $(x + 2)(x + 3)$?
33. Factor: $x^2 - 6x + 9$
34. Factor: $x^2 + 9x + 20$
35. Factor: $x^2 + 6x + 9$
36. Solve: $x^2 - x - 12 = 0$
37. Factor: $x^2 - 2x - 8$
38. Factor: $x^2 + 7x + 10$
39. What are the solutions to the quadratic equation $x^2 - 5x + 6 = 0$?
40. What is $(x + 5)(x - 2)$?
41. To expand an expression in a formula, compute: What is $(x+4)(x+1)$?
42. Solve by factoring: What are the solutions to $x^2-1=0$?
43. A rectangular garden has an area represented by $x^2+7x+12$ square feet, where $x$ is the width added in a redesign. Factor: $x^2+7x+12$.
44. A quadratic model leads to the equation $x^2+2x-8=0$. What are the solutions to $x^2+2x-8=0$?
45. A profit model uses the expression $x^2-9x+20$. Which is the correct factorization of $x^2-9x+20$?
46. A simplified area expression is $x^2-16$. Factor: $x^2-16$.
47. A quadratic equation for a design constraint is $x^2-3x-10=0$. What are the solutions to $x^2-3x-10=0$?
48. A ball’s height is modeled by $h(t)=t^2-5t+6$. To find when it hits the ground, solve $t^2-5t+6=0$.
49. Which of the following expressions is equivalent to $x^2 + 2x - 15$?
50. What is the result when $2x^2 - 3x + 4$ is subtracted from $5x^2 + 2x - 1$?
51. Which of the following is equivalent to $(2x - 3)^3$?
52. Factor: $x^2 + 3x - 10$
53. Which is the correct factorization of $x^2 - 5x + 6$?
54. Factor: $x^2 - 8x + 15$
55. What is $(x - 3)(x + 3)$?
56. Which is the correct factorization of $x^2 - 4x - 5$?
57. What is $(x - 3)(x + 2)$?
58. To simplify an algebraic expression in a model, compute: What is $(x-3)(x+6)$?
59. An object is thrown upward from a height of 10 feet. Its height $h$ (in feet) $t$ seconds after it is thrown is modeled by the function $h(t) = -16t^2 + 64t + 10$. What is the height of the object, in feet, 3 seconds after it is thrown?
60. Solve the equation $x^2 - 8x + 15 = 0$ by factoring.
61. Given $f(x)=x^2-2x+1$, what is the value of $f(3)$?
62. A quadratic equation is $x^2+6x+5=0$. What are the solutions to $x^2+6x+5=0$?
63. To expand an expression used in a perimeter calculation, compute: What is $(x+5)(x-2)$?
64. A simplified expression is $x^2+10x+21$. Which is the correct factorization of $x^2+10x+21$?
65. To rewrite an expression in standard form, compute: What is $(x-7)(x-1)$?
66. What is the value of the expression $2x^3 - x^2 + 3x + 5$ when $x = -2$?
67. A rectangular garden has a length that is 3 feet longer than its width. If the perimeter of the garden is 54 feet, what is the area of the garden, in square feet?