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

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

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

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How many solutions does the equation have? 10x x 2 + x + 2 = 0 A) 6 A) 6 B) 5 B) 5 C) 3 C) 3 D) 2 D) 2

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

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Sorry, thats incorrect. Dont add the exponents, but the answer does deal with exponents Click here to go back to #2 Click here to go back to #2 Click here to go back to #2 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 Click here to go back to #2 Click here to go back to #2 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 A) Yes B) No 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 Click here to go to the next question Click here to go to the next question Click here to go to the next question

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

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If factoring by grouping, which terms would you group together to factor x 3 + x 2 + x + 1 A) (x 3 + x 2 ) + (x + 1) A) (x 3 + x 2 ) + (x + 1) B) (x 3 + x) + (x 2 + 1) B) (x 3 + x) + (x 2 + 1) C) (x 3 + 1) + (x 2 + x) C) (x 3 + 1) + (x 2 + x) D) A, B, & C work 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 Click here to go to question #5 Click here to go to question #5 Click here to go to question #5

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This is a correct way to group, but they actually all work. Choices A) (x 3 + x 2 ) + (x + 1) B) (x 3 + x) + (x 2 + 1) make this problem much easier to solve than choice C) (x 3 + 1) + (x 2 + x) Click here to go to question #5 Click here to go to question #5 Click here to go to question #5 Click here to go to question #5

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If you chose to group like this (x 3 + x 2 ) + (x + 1) What would be the next steps? A) x(x 2 + x) + (1 + x)A) x(x 2 + x) + (1 + x) B) x 2 (x + 1) + 1(x + 1) B) x 2 (x + 1) + 1(x + 1) A) x(x 2 + x) + (1 + x)B) x 2 (x + 1) + 1(x + 1) (x)(x 2 + x)(2) (x 2 + 1)(x + 1) (x)(x 2 + x)(2) (x 2 + 1)(x + 1)(x)(x 2 + x)(2)(x 2 + 1)(x + 1)(x)(x 2 + x)(2)(x 2 + 1)(x + 1) C) x 3 (1 + x) + 1(x + 1)C) x 3 (1 + x) + 1(x + 1) D) x 2 (x) + (x + 1) D) x 2 (x) + (x + 1) C) x 3 (1 + x) + 1(x + 1)D) x 2 (x) + (x + 1) (x 3 + 1)(x + 1) x(x 2 + 1) (x 3 + 1)(x + 1) x(x 2 + 1)(x 3 + 1)(x + 1)x(x 2 + 1)(x 3 + 1)(x + 1)x(x 2 + 1)

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Correct Great job! Click here to go to question #6 Click here to go to question #6 Click here to go to question #6 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 Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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Now we have the factored form (x 2 + 1)(x + 1) Are all of the solutions real numbers? A) Yes A) Yes B) No B) No

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Thats correct. (x 2 + 1) gives imaginary solutions & (x + 1) gives a real solution Click here to go on Click here to go on Click here to go on Click here to go on

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Thats incorrect. (x 2 + 1) gives imaginary solutions & (x + 1) gives a real solution Click here to go on Click here to go on Click here to go on Click here to go on

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What are the real solutions to (x 2 + 1)(x + 1) = 0 ? __ __ __ A) 1, B) 1, A) 1, B) 1, __ __ __ C) ±1D) C) ±1D)

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Thats correct! -1 is the only real solution Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

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Sorry, thats not right. Remember to find solutions set each factor equal to zero and solve. Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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Which is the correct graph for x 3 + x 2 + x + 1 A)A) B) B) A)B) C)D) C)D)

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Great job! You must have remembered what graphs with a 3 rd 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 Click here to go to question #9 Click here to go to question #9 Click here to go to question #9

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Youre 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 Click here to go back to graphs Click here to go back to graphs Click here to go back to graphs

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

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How many solutions does the equation have? 4x 6 – 20x 4 = -24x 2 A) 12 A) 12 B) 6 B) 6 C) 4 C) 4 D) 1 D) 1

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Great! Youre thinking now. Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

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No, remember you dont add the exponents. What do the exponents tell us? Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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

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Factor the following x Click here when you have an answer Click here when you have an answer Click here when you have an answer Click here when you have an answer

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Select the answer that you found. If your answer is not below, click below to return to the problem A) (x 2 + 4)(x – 2) B) (x – 2)(x 2 + 2x + 4) C) (x + 2)(x 2 + 2x + 4) D) (x – 2)(x 2 – 2x – 4) A) (x 2 + 4)(x – 2) B) (x – 2)(x 2 + 2x + 4) C) (x + 2)(x 2 + 2x + 4) D) (x – 2)(x 2 – 2x – 4) A) (x 2 + 4)(x – 2) B) (x – 2)(x 2 + 2x + 4) C) (x + 2)(x 2 + 2x + 4) D) (x – 2)(x 2 – 2x – 4) Go back to problem Go back to problem Go back to problem Go back to problem

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Super! Youre doing great and youre half way finished. Click here to go to question #11 Click here to go to question #11 Click here to go to question #11 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 go back to choices Click here to go back to choices Click here to go back to choices Click here to see the problem again

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Not quite, but youre 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 choices Click here to go back to the choices 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 x 3 + 3x x = -30 A) 3 A) 3 B) -3 B) -3 C) 10 C) 10 D) 5 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 havent graphed it try now.) Click here to go to the next problem Click here to go to the next problem Click here to go to the next problem 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 Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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

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Super job! Youre doing great! Click here to go to the next question Click here to go to the next question Click here to go to the next question 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 Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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Which could be the graphical representation of 32x A)B) A)B) C)C) D) D) C)D)

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

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Factor 27x Click here when you have an answer Click here when you have an answer Click here when you have an answer 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 click hereclick here A) (3x – 2)(9x 2 – 2x + 4) A) (3x – 2)(9x 2 – 2x + 4) B) 27(x + 2)(x 2 – 2x + 4) B) 27(x + 2)(x 2 – 2x + 4) C) 27(x – 2)(x 2 + 2x – 4) C) 27(x – 2)(x 2 + 2x – 4) D) (3x 2 – 6)(3x +6) D) (3x 2 – 6)(3x +6)

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

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Which of the following is a solution to the function 2x = 0 A) -3 A) -3 B) 2 B) 2 C) 3 C) 3 D) 9 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 its multiple choice you could have used substitution and tried all possible answers. Click here to go on Click here to go on Click here to go on Click here to go on

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OOPS, thats wrong. Think about possible ways to solve this equation: Here are a few of the ways: - graph, look for x-intercepts - solve algebraically - because its multiple choice you could have used substitution and tried all possible answers. Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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Youre 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 its multiple choice you could have used substitution and tried all possible answers. Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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How many solutions does the following equation have? 2x x = 14x 3 A) 9 A) 9 B) 5 B) 5 C) 3 C) 3 D) 2 D) 2

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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 Click to see part 2 of this problem Click to see part 2 of this problem Click to see part 2 of this problem

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Sorry, thats incorrect. Dont add the exponents, but the answer does deal with exponents Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation 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 Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation

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What are possible solutions to 2x x = 14x 3 A) 0, 2, -2, 3, -3 A) 0, 2, -2, 3, -3 B) 0, 3, 4 B) 0, 3, 4 __ __ __ __ __ C) 0, -2, 2, 3, -3 C) 0, -2, 2, 3, -3 D) -2, 2 D) -2, 2

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

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What are possible solutions to 2x 3 – 5x x = 45 A) 2.5 A) 2.5 B) 2.5, 3, -3 B) 2.5, 3, -3 C) 2.5, -9 C) 2.5, -9 D) No real solutions D) No real solutions

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

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No, think about all the ways that we can find the solution. Then try again, remember not all solutions must be real. If you havent tried graphing click this link to try that method or go back to the problem and try another method. graphing Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

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Were all through, I hope you have a better understanding of solving equations.

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