SOLUTION: ``Write a polynomial function with the given zeros. 1. -1,1,-6 2. 2,-2,-3 3. 2,1,3 4. 2,3,-3,-1 5. 0,-8,2 6. -10,0,2 Please help me. I really do not get this at all.

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Question 122093: ``Write a polynomial function with the given zeros.
1. -1,1,-6
2. 2,-2,-3
3. 2,1,3
4. 2,3,-3,-1
5. 0,-8,2
6. -10,0,2
Please help me. I really do not get this at all.
Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Write the polynomials having the following zeros:
1) -1, 1, 6
If the polynomial has these zeros, then you can write:
x = -1, so x+1 = 0
x = 1, so x-1 = 0
x = 6, so x-6 = 0
This means that:
Multiply these factors using FOIL to get the generating polynomial:
= This is the polynomial.
Using the same technique:
2) 2, -2, -3
If the polynomial has these zeros, then you can write:
x = 2, so x-2 = 0
x = -2, so x+2 = 0
x = -3, so x+3 = 0
This means that:
Multiply these factors using FOIL to get the generating polynomial:
= This is the polynomial.
Do get the idea?
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

This is an answer I posted previously giving the process for solving these problems.


I'll do one of these to show you the process and then you can do the rest.

If -1, 1, 1, and -6 are zeros of a polynomial, then

 => 
  => 
  => 
 => 

Therefore, the polynomial must be:






And the function would then be 

Use the same method to solve all of the rest.  The degree of the resulting
polynomial (the highest power on x) must equal the number of roots given
if you have done the work properly.


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