how do solve 3x^3+2x^2-12x-8=0

- Anguyennn

how do solve 3x^3+2x^2-12x-8=0

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- zepdrix

Ooo I think this one is going to work out nicely with grouping! :)

- Anguyennn

how do you do that?

- Anguyennn

yes that is what the question is asking me to do actually haha :)

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## More answers

- zepdrix

Oh interesting c: hah

- zepdrix

\[\large\rm \color{#DD4747}{3x^3-12x}+\color{#3366CF}{2x^2-8}=0\]Notice that the cubic term and the first degree term are both divisible by 3,
while the squared term and constant term are both even, divisible by 2,
so let's group them like this!

- zepdrix

We want to do some factoring.
What can we factor out of the red guys?
What do they have in common?

- Anguyennn

\[\large\rm \color{#DD4747}{3x^3-12x}+\color{#3366CF}{2x^2-8}=0\]

- Anguyennn

all i see is that

- Anguyennn

I don't see any equations

- zepdrix

The equation didn't show up for you?
Are you using Internet Explorer or some junk like that? :c lol

- Anguyennn

I am using safari

- zepdrix

oh boy :( hmm

- zepdrix

Reload browser? :o
Maybe the plugin just crashed for you or something

- Anguyennn

ok please hold on ok

- Anguyennn

oh yes i see it now!!

- zepdrix

yay c:

- Anguyennn

so it would be (3x+2) (x^2-4)

- zepdrix

Oh, you did it all the way already XD haha nice!

- Anguyennn

so would the final answer be x=2/3, -2, 2?

- zepdrix

-2/3, ya? :)
Gotta subtract the 2 over

- Anguyennn

oh!!!

- Anguyennn

but wait, what about x^3-8x^2=0

- zepdrix

Oh this is another problem? I see :)

- Anguyennn

this is another one

- Anguyennn

yes

- zepdrix

So they each have at least two x's, multiplying, ya?
So we can pull an x^2 out of each.

- zepdrix

\[\large\rm x^2(x-8)=0\]Something like that, ya? :d

- Anguyennn

yes

- zepdrix

Apply your `Zero-Factor Property` again :)
\(\large\rm x^2=0\) and \(\large\rm x-8=0\)
and solve for x in each case.

- Anguyennn

I know one of them would be x=8

- Anguyennn

but what about for the x^2? that is what i am confused about

- zepdrix

\(\large\rm x^2=0\)
Take square root,
\(\large\rm \pm x=0\)
Leading to,
\(\large\rm x=0\)

- zepdrix

square root of zero is... zero :) ya?

- Anguyennn

yes

- Anguyennn

but when you square root x it becomes 10

- zepdrix

?

- Anguyennn

oh wait never mind, i am talking nonsense

- zepdrix

x is being squared.
we perform the `opposite` operation of squaring to remove the square.
square root is the opposite of squaring.
So when we apply the square root, they `undo` one another.

- Anguyennn

wow thanks I understand it now!!

- zepdrix

yay team \c:/

- Anguyennn

are you able to help me with some other questions since you are here already :P

- Anguyennn

you are a really great help btw thank you i appreciate it

- zepdrix

uh sure +_+

- zepdrix

you can post it,
i gotta make some food real quick :D brb

- Anguyennn

##### 1 Attachment

- Anguyennn

##### 1 Attachment

- Anguyennn

I am not sure how to do c, f, or g.

- zepdrix

What did you get for b?
Your profit function.

- Anguyennn

I got 13.83n-102.4

- Anguyennn

I showed you a picture as well

- Anguyennn

the second document

- zepdrix

oh lol :)

- Anguyennn

yup :)

- zepdrix

Since this is a `linear function`,
\(\large\rm \text{rate of change = slope}\)
So the slope of your P(n) function is your rate of change.

- Anguyennn

how do you find out the slope? mx+b?

- zepdrix

Yes, m :)

- zepdrix

We can write the number like this if it makes things easier:\[\large\rm m=\frac{13.83}{1}\]Remember that slope is `rise over run`.
So I would like two separate numerical values in my slope so I can interpret it.
The 13.83 represents profit,
the 1 represents 1 pizza sold.
So this value represents the amount of profit made per pizza!

- Anguyennn

hmm

- Anguyennn

so would 1 be the y coordinate on the graph?

- zepdrix

slope is `change in y` divided by `change in x`.
So the bottom number is the x ( n in this case ).

- Anguyennn

oh ok thank you so much for your help!

- Anguyennn

until next time :)

- zepdrix

`practical domain`
You don't want to open a pizza shop and sell two pizzas every day.
You'll end up losing money because of your operating costs!
So you want your domain to start from the `break-even point`.

- Anguyennn

which is going to be n=7.40?

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