Andrew M. answered • 11/06/16

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

f(x)=-.0029(x+12)(x+5)

^{2}(x-9)^{3}Michael is correct that the multiplicity has to do with the exponents.

If you write this out all the way your expanded polynomial is:

f(x) = -.0029(x+12)(x+5)(x+5)(x-9)(x-9)(x-9)

The zero at x=-12 appears 1 time so has a multiplicity of 1.

You can see that the zero at x=-5 appears 2 times and has multiplicity 2.

What about the other zero?

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NOTE:

If this was multiplied out you would have a polynomial of degree 6,

meaning the highest exponent on a variable would be on the x

^{6}. Basedon that you would expect there to be 6 zeroes. Here we see only 3 ...

{-12, -5, 9} ... With this polynomial we have 6 zeroes in actuality, but

3 of the zeroes are "repeats" due to the multiplicity of the zeroes at

x=-5 and x=9.