SOLUTION: how do you find a polynomial of degree 4 with -2 as a zero of multiplicity 2 and 0 and 3 as zeros of multiplicity 1

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Question 524522: how do you find a polynomial of degree 4 with -2 as a zero of multiplicity 2 and 0 and 3 as zeros of multiplicity 1
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
how do you find a polynomial of degree 4 with -2 as a zero
of multiplicity 2 and 0 and 3 as zeros of multiplicity 1.
Make a row of equations with x = each of the zeros, 
as many times as their multiplicities:

      x = -2,       x = -2,    x = 0,        x = 3

Get 0 on the right of each equation:

  x + 2 = 0     x + 2 = 0      x = 0,    x - 3 = 0  

Write the product of all the left sides:

         (x + 2)(x + 2)(x)(x - 3) = 0

Multiply them all together:

           (x2 + 4x + 4)(x2 - 3x) = 0

x4 - 3x3 + 4x3 - 12x2 + 4x2 - 12x = 0 

Collect like terms

              x4 + x3 - 8x2 - 12x = 0 

Set P(x) = the left side:

          P(x) = x4 + x3 - 8x2 - 12x

Edwin