Originally Posted by

**mikedwd** the root negetive root three has a multiplicity of 2

the root two has a multiplicity of 4

if you set each factor equal to zero and solve for x, that gives you the root from factored form

the exponent that the factor is raised to is the multiplicity, because that is the number of times that that factor is a factor of the polynomial (maybe it's easier to understand if i show you an example:

x(squared)-4x+4

factors to (x-2)(x-2)

which is the same as (x-2)squared

the root is x-2=0 so x=2

so the root x=2 has a multiplicity of 2 in my example)

in your situation there is a root (x-2) raised to the 4th, so the root x=2 has a multiplicity of 4