You are having a meeting with the CEO of a soda company. You have interpreted the number of cans of soda produced versus profit as the function P(x) = x4 − x3 − 11x2 + 9x + 18. Describe to the CEO what the graph looks like and, in general, how to sketch the graph without using technology. Use complete sentences, and focus on the end behaviors of the graph and where the company will break even (where P(x) = 0).

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- anonymous

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- Keigh2015

U don't know this one I am sorry

- Keigh2015

*I

- anonymous

ok

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## More answers

- radar

Attempt to factor the function using synthetic division. Looking at the numerical term (18) use some of the prime factors 3 and 2 and also try 1.

- anonymous

So ok Im a little confused

- anonymous

nvm I get it hold on

- anonymous

so it wouldn't be 1 because you don't get a remainder of 0

- anonymous

@radar ?

- anonymous

Ok I'm honestly confused.

- anonymous

- anonymous

@jane11509 @just_one_last_goodbye

- radar

|dw:1435938115440:dw|
I used long division as you are confused and probably don't understand synthetic division. As you can see one of the zero crossings would be x = -1. Now factor the x3-2x2-9x+18 using the numbers I have given you that are the prime factors of 18. Hint try 3.

- radar

The -3 and + 3 or (x+3)(x-3) are correct and since x-2 = 0, the function would cross the x axis at (2,0) Since you know it is a fourth degtree equation there is another root, it will be equal to one that I have already provided but of opposite sign.

- radar

Do you know synthetic division?

- anonymous

Yes

- anonymous

what do I do now

- anonymous

@radar Is that it?

- radar

Test both signs of 1 for a zero. Use synthetic division.

- radar

Yes the 4 cross over points are -1, +3, -3 and 2. Mark them on your graph those are the x values and of course P9x) would equal 0 at those points. Let x = 0 and plot P(x) That is the pointy where the graph crosses the P(x) or Y axis.

- radar

You should now be able to show where the company is breaking even also where the company is losing money. Do what the problem asks.

- anonymous

How would u graph this without using technology?

- anonymous

i mean finding the end behaviors when the company breaks even P(X)=0

- radar

Well without technology, you would have to use knowledge.
Knowledge of 4th degree polynomial.
knowing that it would have 4 roots.
knowing how to plug in a value and solve for the function to get the P(x)
Knowing how the sign of P(x) changes at 0 crossings,
In other words study your text and course material.
Good luck with your studies.

- radar

I have just told you when the company breaks even, that was what we were doing when we got the roots (zero value of P(x).

- anonymous

ohhh :)

- radar

That is not the end behavior for the company breaking even! The end behavior is the limits of the function and they are infinite .........Positive for all values of x greater than 3.

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