1. Click here to go to question #1
Please answer the following multiple choice questions. Click on your answer. Please feel free to use paper or graphing calculators to find the correct answer.
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2. When finding solutions to equations, you are finding the
A) x-intercepts
B) y-intercepts
C) vertex points
D) line of symmetry

3. Correct! Great job!
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4. OOPS Please try again.
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5. How many solutions does the equation have? 10x3 + 20x2 + x + 2 = 0
B) 5
C) 3
D) 2

6. Right! You knew to look for the highest degree of exponent.
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7. Sorry, that’s incorrect
Sorry, that’s incorrect. Don’t add the exponents, but the answer does deal with exponents
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8. OOPS Try again, but think about what the exponents tell us.
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9. Do all of the solutions to these problems have to be real number solutions?
A) Yes
B) No

10. Correct! They can have a combination of real and imaginary solutions!
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11. That’s incorrect. Remember they can have a combination of real and imaginary solutions.
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12. If factoring by grouping, which terms would you group together to factor x3 + x2 + x + 1
A) (x3 + x2) + (x + 1)
B) (x3 + x) + (x2 + 1)
C) (x3 + 1) + (x2 + x)
D) A, B, & C work

13. Super! Although they all work, choices A and B make this problem much easier to solve.
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14. This is a correct way to group, but they actually all work
This is a correct way to group, but they actually all work. Choices A) (x3 + x2) + (x + 1) B) (x3 + x) + (x2 + 1) make this problem much easier to solve than choice C) (x3 + 1) + (x2 + x)
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15. If you chose to group like this (x3 + x2) + (x + 1) What would be the next steps?
A) x(x2 + x) + (1 + x) B) x2(x + 1) + 1(x + 1)
(x)(x2 + x)(2) (x2 + 1)(x + 1)
C) x3(1 + x) + 1(x + 1) D) x2(x) + (x + 1)
(x3 + 1)(x + 1) x(x2 + 1)

16. Correct Great job!
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17. OOPS Please look at all the choices and try again.
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18. Now we have the factored form (x2 + 1)(x + 1) Are all of the solutions real numbers?
A) Yes
B) No

19. That’s correct. (x2 + 1) gives imaginary solutions & (x + 1) gives a real solution
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20. That’s incorrect. (x2 + 1) gives imaginary solutions & (x + 1) gives a real solution
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21. What are the real solutions to (x2 + 1)(x + 1) = 0 ?__
A) 1, -1 B) √1, -1
C) ±√1 D) -1

22. That’s correct! -1 is the only real solution
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23. Sorry, that’s not right. Remember to find solutions set each factor equal to zero and solve.
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24. Which is the correct graph for x3 + x2 + x + 1
A) B)
C) D)

25. Great job! You must have remembered what graphs with a 3rd degree polynomial look like, then you only had to remember the real solution to figure it out. Or You used your graphing calculator.
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26. You’re close but remember what the real solution was to this problem
You’re close but remember what the real solution was to this problem. We solved it in the last question.
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27. That’s incorrect. Think about what shape the graph of a 3rd degree polynomial should look like.
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28. How many solutions does the equation have? 4x6 – 20x4 = -24x2
B) 6
C) 4
D) 1

29. Great! You’re thinking now.
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30. No, remember you don’t add the exponents. What do the exponents tell us?
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31. Sorry that’s incorrect. What do the exponents tell us?
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32. Factor the following x3 - 8
Click here when you have an answer

33. Select the answer that you found
Select the answer that you found. If your answer is not below, click below to return to the problem A) (x2 + 4)(x – 2) B) (x – 2)(x2 + 2x + 4) C) (x + 2)(x2 + 2x + 4) D) (x – 2)(x2 – 2x – 4)
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34. Super! You’re doing great and you’re half way finished.
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35. No, think about the rules for factoring the difference of cubes.
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36. Not quite, but you’re close
Not quite, but you’re close. Think about the signs that you need when factoring the difference of cubes.
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37. Which of the following are possible solutions to the function x3 + 3x2 + 10x = -30
D) 5

38. Great job! Did you remember that there are several ways to get this solution. If you factored and then set them equal to zero, you could have checked your answer by graphing the equation, and finding the x-intercepts. (If you haven’t graphed it try now.)
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39. No, please try again. Hint 1: set the equation equal to zero Hint 2: factor, set each equal to zero and solve Hint 3: graph and look at the x-intercepts
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40. Find one possible solution to the equation below -2x3 – 4x2 – 3x – 6 = 0
C) -2
D) No real solutions

41. Super job! You’re doing great!
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42. No, please try again. Hint 1: factor, set each equal to zero and solve Hint 2: graph and look at the x-intercepts
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43. Which could be the graphical representation of 32x3 - 4
A) B)
C) D)

44. Correct! Great job!
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45. No, think about what shape the graph of a cubic should look like.
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46. No, but you have the right shape.
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47. Factor 27x
Click here when you have an answer

48. Select your answer, if it is not here click here to go back to the problem so you may try again
A) (3x – 2)(9x2 – 2x + 4)
B) 27(x + 2)(x2 – 2x + 4)
C) 27(x – 2)(x2 + 2x – 4)
D) (3x2 – 6)(3x +6)

49. Super job! You remembered everything, you must be thinking.
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50. No, please try again. Taking out the GCF might be a good start.
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51. You remembered to take out the GCF, but check your signs.
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52. Which of the following is a solution to the function 2x3 + 54 = 0
B) 2
C) 3
D) 9

53. Correct, great job. There were several ways to come up with this answer. Here are a few of the ways: - graph, look for x-intercepts - solve algebraically - because it’s multiple choice you could have used substitution and tried all possible answers.
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54. OOPS, that’s wrong. Think about possible ways to solve this equation: Here are a few of the ways: - graph, look for x-intercepts - solve algebraically - because it’s multiple choice you could have used substitution and tried all possible answers.
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55. You’re very close, go back and check your work
You’re very close, go back and check your work. You may also want to try it another way, such as: - graph, look for x-intercepts - solve algebraically - because it’s multiple choice you could have used substitution and tried all possible answers.
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56. How many solutions does the following equation have? 2x5 + 24x = 14x3
B) 5
C) 3
D) 2

57. Great job. You knew it was the largest exponent
Great job! You knew it was the largest exponent. Did you also remember that not all solutions have to be real solutions?
Click to see part 2 of this problem

58. Sorry, that’s incorrect
Sorry, that’s incorrect. Don’t add the exponents, but the answer does deal with exponents
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59. OOPS Try again, but think about what the exponents tell us.
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60. What are possible solutions to 2x5 + 24x = 14x3
__ __
C) 0, -2, 2, √3, -√3
D) -2, 2

61. Super! Did you solve this algebraically, graphically, or by using the solutions that were given? If you only tried one method, try another before you move on.
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62. No, please try again. Hint: Check your math or try to solve the problem another way (graphically).
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63. What are possible solutions to 2x3 – 5x2 + 18x = 45
C) 2.5, -9
D) No real solutions

64. Super job! There is only 1 real solution, the other 2 are imaginary.
Click here, please

65. No, think about all the ways that we can find the solution
No, think about all the ways that we can find the solution. Then try again, remember not all solutions must be real. If you haven’t tried graphing click this link to try that method or go back to the problem and try another method.
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66. We’re all through, I hope you have a better understanding of solving equations.