Jordan H.

# Polynomial Functions - Zeroes and Multiplicity

A polynomial function has zeros at 5/2 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function in standard form that could represent this function.

I'm confused as to how to work this out, any help would be greatly appreciated.

## 3 Answers By Expert Tutors

By: Math and Computer Programming Guide Christopher A.

tutor
Note: the problem asks us to write a function that *could* represent the function described by the zeros. Because the zeros do not determine a unique polynomial, we are only providing one possible representation.
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12/09/19

Donovan B.

True, both of our solutions are correct depending on how you initialize the problem. In the end, both equations would represent the function above. Isn't math so FUN!!!
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12/09/19 Arturo O.

Quite true. Often, these problems include a statement like f(2) = 16, so we can get a unique solution, or maybe the leading coefficient is stated in the problem. Without information like that, there are infinitely many polynomials with this set of zeros and multiplicities.
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12/09/19 Christopher A.

tutor
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12/09/19

Your mind can achieve great things! Christopher A.

tutor
On the last line, the second term should be -8x^6.
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12/09/19

Donovan B.

Oh wow, didn't notice the typo Thanks
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12/09/19 