SOLUTION: Form a polynomial function Zeros: -2, multiplicity 2;4, multiplicity 1; degree 3

Question 661682: Form a polynomial function Zeros: -2, multiplicity 2;4, multiplicity 1; degree 3
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
One answer is

You could multiply the whole thing by any non-zero number to get another solution.

To have for a zero with multiplicity ,
a polynomial must have as a factor times.
An example would be , but we can multiply that by any factor,
other than zero, and would still be a zero with multiplicity .

To get as a zero, you need the factor
To get as a zero with multiplicicty , you need to include as a factor

To get as a zero, you need the factor

To have both,
as a zero with multiplicicty ,
and as a zero with multiplicicty ,
you need to include as a factor.

Since
is a polynomial of degree 3, you cannot include any other factors with the variable ,
but you can multiply that polynomial by any real number other than zero,
and it will still be a polynomial of degree 3, with the required zeros.
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