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.

Question

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.

misty1212 · Answer

HI!!

anonymous · Answer

Hello!

misty1212 · Answer

if 0 is a zero with "multiplicity 2" that means one factor is $x^2$

anonymous · Answer

but 2 is also a zero that has a factor of x^2, right?

misty1212 · Answer

no

misty1212 · Answer

since 2 is a zero, one factor is $x-2$

misty1212 · Answer

since it is a zero with "multiplicity" 2 there are two of those factors, i.e. $(x-2)^2$

misty1212 · Answer

do you know what "multiplicity " means here?

anonymous · Answer

I believe that multiplicity is the exponent value.

anonymous · Answer

Right? or am i mistaken.

misty1212 · Answer

yes that is right

misty1212 · Answer

so if $r$ is a zero with multiplicity $n$ then one factor is $(x-r)^n$

anonymous · Answer

Ok, that makes more sense. I don't know why I was so confused. Thank you!