SOLUTION: Find all real zeros of the polynomial function. Determine the multiplicity of each zero. f(x)=x^3(x-3)^3

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Question 443767: Find all real zeros of the polynomial function. Determine the multiplicity of each zero.
f(x)=x^3(x-3)^3

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3(x-3)^3
The zeros of the function are the values of x which make f(x) = 0:
x^3(x-3)^3 = 0
The LHS will be equal to 0 if x = 0, or x = 3. The latter has a multipicity of 3.
So the zeros are: 0, 3 (multiplicity 3)
The graph is shown below:
graph%28400%2C400%2C-6%2C6%2C-20%2C20%2Cx%5E3%2A%28x-3%29%5E3%29