The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3 Find a possible formula for P(x). I understand what multiplicity is, my question would be is that it says BOTH x=2 and x=0 have a multiplicity of 2, that doesnt make any sense to me.

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The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=2 and x=0, and a root of multiplicity 1 at x=−3 Find a possible formula for P(x). I understand what multiplicity is, my question would be is that it says BOTH x=2 and x=0 have a multiplicity of 2, that doesnt make any sense to me.

Mathematics
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HI!!
Hello!
if 0 is a zero with "multiplicity 2" that means one factor is \(x^2\)

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but 2 is also a zero that has a factor of x^2, right?
no
since 2 is a zero, one factor is \(x-2\)
since it is a zero with "multiplicity" 2 there are two of those factors, i.e. \((x-2)^2\)
do you know what "multiplicity " means here?
I believe that multiplicity is the exponent value.
Right? or am i mistaken.
yes that is right
so if \(r\) is a zero with multiplicity \(n\) then one factor is \((x-r)^n\)
Ok, that makes more sense. I don't know why I was so confused. Thank you!

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