## Presentation on theme: "Click here to go to question #1"— Presentation transcript:

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

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.

Sorry, that’s incorrect

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

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!

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

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.

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)

OOPS Please look at all the choices and try again.

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

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

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

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

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.

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

Great! You’re thinking now.

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

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

Factor the following x3 - 8

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.

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

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!

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)

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

No, but you have the right shape.

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.

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

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

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

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

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).

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.