What is a polynomial function in standard form with zeroes 1, 2, 3, and –3?

Question

anonymous · Answer

I have no idea how to do this

retireed · Answer

You have been given the roots.  You just need to find "factors" that have cancelling values, when set equal to zero.

Words I know that don't make much sense.  I will simplify in the next example.

retireed · Answer

(x+3)(x-7)  are factors of the polynomial
      
      x^2 - 4x -21

      the ROOTs   are   x + 3 = 0   x = -3
                                 x -  7 = 0   x =  7

      the roots are -3, and 7

     You were given the ROOTs you just need to work BACKWARDs

     ALSO you were given 4 ROOTs which will be more difficult when it comes to multiply the 3 or 4 factors out to get the polynomial in standard form.

anonymous · Answer

So would the answer be x^4-3x^3-7x^2+27x-18 = 0

anonymous · Answer

?

retireed · Answer

Why did I say 3 or 4 factors?  Is because ONE of the factors is a double root.  I think that is the term.

retireed · Answer

summer that could be the answer, but I haven't gotten that far yet.  

How did you get that answer?  

What factors did you multiply?

anonymous · Answer

3 and -3 is the double root then?

retireed · Answer

YES

misty1212 · Answer

hmm

retireed · Answer

Factor 1  (x^2 - 3)

misty1212 · Answer

not to butt in, but if 3 was  a "double root' or a zeros of multiplicity two would have the factor $(x-3)^2$

anonymous · Answer

So its not a double root?

misty1212 · Answer

and if one factor was $x^2-3$ then the zeros would be $\sqrt3$ and $-\sqrt3$

anonymous · Answer

But was my answer right?

misty1212 · Answer

idk i didn't do it, you want me to check?

anonymous · Answer

yes, I will also tell you how I did it

misty1212 · Answer

your answer is correct

retireed · Answer

Misty you are right, I am working without paper, so my brain might not be seeing the whole picture.  Thanks for your help.

anonymous · Answer

I tested multiplying by the factors which were 1,2,3,6,9,18. The coefficient is 1 and the trailing coefficient is -18.

anonymous · Answer

-3, 1,2, and 3 are the only ones who got zero as a result

retireed · Answer

Now I'm really confused, sorry.

anonymous · Answer

It's okay if you can't help, I can just ask my teacher

anonymous · Answer

Thanks anyways :)

retireed · Answer

Let's get the easy factors.

retireed · Answer

1, 2, 3, and –3

   (x -1) (x -2) (x -3) (x +3)     these makes more sense  Can you do this?

Multiply these out to get the standard form for the polynomial.  My double root thought got me confused.