Find a cubic function with the given zeros. You must show your work

-2, 3, -3

Question

Find a cubic function with the given zeros. You must show your work

-2, 3, -3

allank · Answer

Hint: If x=a and x=b are the zeros of a function, then the function is (x-a)(x-b)

anonymous · Answer

im lost :(

allank · Answer

An example always helps. 
Take the function f(x)=x^2-5x+6
Can you calculate the zeros of that function?

allank · Answer

Still there @babydoll332 ?

anonymous · Answer

12,-10

anonymous · Answer

start with 
$$(x+2)(x-3)(x+3)$$ and multiply this mess out to get your answer

anonymous · Answer

way would i multiply with?

anonymous · Answer

**what

anonymous · Answer

i mean to multiply these factors together

allank · Answer

f(x)=x^2-5x+6
You need to factorize it to get
f(x) = (x-3)(x-2)
Then the zeros become 3 and 2. 
Now, what @satellite73  is telling you is to do the reverse. Does that help?

anonymous · Answer

start by multiplying $(x+3)(x-3)$ and when you are done, multiply the result by $x+2$

anonymous · Answer

3x^2+4x-9

anonymous · Answer

no I'm so completely LOST

allank · Answer

Okay, do you understand why the function will be (x+2)(x-3)(x+3)?

anonymous · Answer

yes

allank · Answer

Wonderful. so you only have a problem with the multiplication?

anonymous · Answer

the anserw is this right 3x^2+4x-9 of (x+2)(x-3)(x+3)

allank · Answer

Lemme work it out here:
(x+2)(x-3)(x+3) = (x^2-3x+2x-6)(x+3) = x^3+3x^2-3x^2-6x+2x^2+6x-6x-6

anonymous · Answer

ok then?

allank · Answer

So, put like terms together and simplify. 
x^3+3x^2-3x^2-6x+2x^2+6x-6x-6
x^3+2x^2-6

anonymous · Answer

not to butt in, but it would be somewhat simpler to multiply $(x+3)(x-3)$ first because you end up with only two terms

anonymous · Answer

$(x+3)(x-3)=x^2+3x-3x-9=x^2-9$

allank · Answer

True, @satellite73  =)

anonymous · Answer

then multiply $(x^2-9)(x+2)=x^2+2x^2-9x-18$

anonymous · Answer

no like terms to collect, and you are done at that step

anonymous · Answer

except i made a typo, it should be $$(x^2-9)(x+2)=x^3+2x^2-9x-18$$

anonymous · Answer

ohh ok i get it then way do i do

anonymous · Answer

?

allank · Answer

Choose the method you are more comfortable with. Both are okay. Just two ways of doing the same thing. :)

anonymous · Answer

so after i do that I'm done?

anonymous · Answer

?

allank · Answer

Yes

anonymous · Answer

thank u

allank · Answer

You're welcome