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**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. Click here to go to question #1

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**When finding solutions to equations, you are finding the**

A) x-intercepts B) y-intercepts C) vertex points D) line of symmetry

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Correct! Great job! Click here to go to the next question

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OOPS Please try again. Click here to return to Question #1

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**How many solutions does the equation have? 10x3 + 20x2 + x + 2 = 0**

B) 5 C) 3 D) 2

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**Right! You knew to look for the highest degree of exponent.**

Click here to go to question #3

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**Sorry, that’s incorrect**

Sorry, that’s incorrect. Don’t add the exponents, but the answer does deal with exponents Click here to go back to #2

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**OOPS Try again, but think about what the exponents tell us.**

Click here to go back to #2

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**Do all of the solutions to these problems have to be real number solutions?**

A) Yes B) No

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**Correct! They can have a combination of real and imaginary solutions!**

Click here to go to the next question

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**That’s incorrect. Remember they can have a combination of real and imaginary solutions.**

Click here to go to the next question

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**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

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**Super! Although they all work, choices A and B make this problem much easier to solve.**

Click here to go to question #5

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**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) Click here to go to question #5

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**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)

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Correct Great job! Click here to go to question #6

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**OOPS Please look at all the choices and try again.**

Click here to go back to the problem

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**Now we have the factored form (x2 + 1)(x + 1) Are all of the solutions real numbers?**

A) Yes B) No

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**That’s correct. (x2 + 1) gives imaginary solutions & (x + 1) gives a real solution**

Click here to go on

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**That’s incorrect. (x2 + 1) gives imaginary solutions & (x + 1) gives a real solution**

Click here to go on

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**What are the real solutions to (x2 + 1)(x + 1) = 0 ?**

__ A) 1, -1 B) √1, -1 C) ±√1 D) -1

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**That’s correct! -1 is the only real solution**

Click here to go to the next question

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**Sorry, that’s not right. Remember to find solutions set each factor equal to zero and solve.**

Click here to go back to the problem

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**Which is the correct graph for x3 + x2 + x + 1**

A) B) C) D)

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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. Click here to go to question #9

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**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. Click here to go back to graphs

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**That’s incorrect. Think about what shape the graph of a 3rd degree polynomial should look like.**

Click here to go back to graphs

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**How many solutions does the equation have? 4x6 – 20x4 = -24x2**

B) 6 C) 4 D) 1

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**Great! You’re thinking now.**

Click here to go to the next question

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**No, remember you don’t add the exponents. What do the exponents tell us?**

Click here to go back to the problem

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**Sorry that’s incorrect. What do the exponents tell us?**

Click here to go back to the problem

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**Factor the following x3 - 8**

Click here when you have an answer

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**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) Go back to problem

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**Super! You’re doing great and you’re half way finished.**

Click here to go to question #11

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**No, think about the rules for factoring the difference of cubes.**

Click here to go back to choices Click here to see the problem again

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**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. Click here to go back to the choices Click here to go back to the problem

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**Which of the following are possible solutions to the function x3 + 3x2 + 10x = -30**

D) 5

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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.) Click here to go to the next problem

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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 Click here to go back to the problem

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**Find one possible solution to the equation below -2x3 – 4x2 – 3x – 6 = 0**

C) -2 D) No real solutions

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**Super job! You’re doing great!**

Click here to go to the next question

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No, please try again. Hint 1: factor, set each equal to zero and solve Hint 2: graph and look at the x-intercepts Click here to go back to the problem

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**Which could be the graphical representation of 32x3 - 4**

A) B) C) D)

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Correct! Great job! Click here to go to the next question

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**No, think about what shape the graph of a cubic should look like.**

Click here to go back to the graphs

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**No, but you have the right shape.**

Click here to go back to the graphs

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Factor 27x Click here when you have an answer

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**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)

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**Super job! You remembered everything, you must be thinking.**

Click here to go on

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**No, please try again. Taking out the GCF might be a good start.**

Click here to go back to answers Click here to go back to the problem

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**You remembered to take out the GCF, but check your signs.**

Click here to go back to the problem Click here to go back to answers

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**Which of the following is a solution to the function 2x3 + 54 = 0**

B) 2 C) 3 D) 9

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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. Click here to go on

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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. Click here to go back to the problem

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**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. Click here to go back to the problem

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**How many solutions does the following equation have? 2x5 + 24x = 14x3**

B) 5 C) 3 D) 2

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**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

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**Sorry, that’s incorrect**

Sorry, that’s incorrect. Don’t add the exponents, but the answer does deal with exponents Click here to go back to the equation

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**OOPS Try again, but think about what the exponents tell us.**

Click here to go back to the equation

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**What are possible solutions to 2x5 + 24x = 14x3**

__ __ C) 0, -2, 2, √3, -√3 D) -2, 2

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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. Click here to go to the last question Click here to go back and see the original equation

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**No, please try again. Hint: Check your math or try to solve the problem another way (graphically).**

Click here to go back to the equation

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**What are possible solutions to 2x3 – 5x2 + 18x = 45**

C) 2.5, -9 D) No real solutions

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**Super job! There is only 1 real solution, the other 2 are imaginary.**

Click here, please

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**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. Click here to go back to the problem

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**We’re all through, I hope you have a better understanding of solving equations.**

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