Question

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

Answer 1

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

Answer 2

how do you do that?

Answer 3

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

Answer 4

Oh interesting c: hah

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

all i see is that

Answer 9

I don't see any equations

Answer 10

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

Answer 11

I am using safari

Answer 12

oh boy :( hmm

Answer 13

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

Answer 14

ok please hold on ok

Answer 15

oh yes i see it now!!

Answer 16

yay c:

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

oh!!!

Answer 22

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

Answer 23

Oh this is another problem? I see :)

Answer 24

this is another one

Answer 25

yes

Answer 26

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

Answer 27

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

Answer 28

yes

Answer 29

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

Answer 30

I know one of them would be x=8

Answer 31

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

Answer 32

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

Answer 33

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

Answer 34

yes

Answer 35

but when you square root x it becomes 10

Answer 36

?

Answer 37

oh wait never mind, i am talking nonsense

Answer 38

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.

Answer 39

wow thanks I understand it now!!

Answer 40

yay team \c:/

Answer 41

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

Answer 42

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

Answer 43

uh sure +_+

Answer 44

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

Answer 45

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

Answer 46

What did you get for b?
Your profit function.

Answer 47

I got 13.83n-102.4

Answer 48

I showed you a picture as well

Answer 49

the second document

Answer 50

oh lol :)

Answer 51

yup :)

Answer 52

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.

Answer 53

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

Answer 54

Yes, m :)

Answer 55

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!

Answer 56

hmm

Answer 57

so would 1 be the y coordinate on the graph?

Answer 58

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

Answer 59

oh ok thank you so much for your help!

Answer 60

until next time :)

Answer 61

`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`.

Answer 62

which is going to be n=7.40?