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

When finding solutions to equations, you are finding the A) x-intercepts B) y-intercepts C) vertex points D) line of symmetry

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

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

How many solutions does the equation have? 10x3 + 20x2 + x + 2 = 0 B) 5 C) 3 D) 2

Right! You knew to look for the highest degree of exponent. Click here to go to question #3

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

OOPS Try again, but think about what the exponents tell us. Click here to go back to #2

Do all of the solutions to these problems have to be real number solutions? A) Yes B) No

Correct! They can have a combination of real and imaginary solutions! Click here to go to the next question

That’s incorrect. Remember they can have a combination of real and imaginary solutions. Click here to go to the next question

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

Super! Although they all work, choices A and B make this problem much easier to solve. Click here to go to question #5

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

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)

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

OOPS Please look at all the choices and try again. Click here to go back to the problem

Now we have the factored form (x2 + 1)(x + 1) Are all of the solutions real numbers? A) Yes B) No

That’s correct. (x2 + 1) gives imaginary solutions & (x + 1) gives a real solution Click here to go on

That’s incorrect. (x2 + 1) gives imaginary solutions & (x + 1) gives a real solution Click here to go on

What are the real solutions to (x2 + 1)(x + 1) = 0 ? __ A) 1, -1 B) √1, -1 C) ±√1 D) -1

That’s correct! -1 is the only real solution Click here to go to the next question

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

Which is the correct graph for x3 + x2 + x + 1 A) B) C) D)

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

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

That’s incorrect. Think about what shape the graph of a 3rd degree polynomial should look like. Click here to go back to graphs

How many solutions does the equation have? 4x6 – 20x4 = -24x2 B) 6 C) 4 D) 1

Great! You’re thinking now. Click here to go to the next question

No, remember you don’t add the exponents. What do the exponents tell us? Click here to go back to the problem

Sorry that’s incorrect. What do the exponents tell us? Click here to go back to the problem

Factor the following x3 - 8 Click here when you have an answer

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

Super! You’re doing great and you’re half way finished. Click here to go to question #11

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

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

Which of the following are possible solutions to the function x3 + 3x2 + 10x = -30 D) 5

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

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

Find one possible solution to the equation below -2x3 – 4x2 – 3x – 6 = 0 C) -2 D) No real solutions

Super job! You’re doing great! Click here to go to the next question

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

Which could be the graphical representation of 32x3 - 4 A) B) C) D)

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

No, think about what shape the graph of a cubic should look like. Click here to go back to the graphs

No, but you have the right shape. Click here to go back to the graphs

Factor 27x3 + 216 Click here when you have an answer

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)

Super job! You remembered everything, you must be thinking. Click here to go on

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

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

Which of the following is a solution to the function 2x3 + 54 = 0 B) 2 C) 3 D) 9

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

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

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

How many solutions does the following equation have? 2x5 + 24x = 14x3 B) 5 C) 3 D) 2

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

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

OOPS Try again, but think about what the exponents tell us. Click here to go back to the equation

What are possible solutions to 2x5 + 24x = 14x3 __ __ C) 0, -2, 2, √3, -√3 D) -2, 2

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

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

What are possible solutions to 2x3 – 5x2 + 18x = 45 C) 2.5, -9 D) No real solutions

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

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

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