Math question about zeros of polynomial functions?
Here goes: "Definition of multiple zeros of a polynomial function." If a polynomial function P has (x-r) as a factor exactly k times, then r is a zero of multiplicity k of the polynomial function P.
Why does this seem as if it is an arbitrary statement? The outcome of the function does not change so why is it important to become aware of the inputs? I want to know where I am going to see this later on so I can recognize it better then as well as understand it 100%.
An example of a problem:
P(x) = (x-5)^2(x+2)^3(x+4)
*5 as a Zero of multiplicity 2
*-2 as a Zero of multiplicity 3
*-4 as a Zero of multiplicity 1
I asked my Prof. and he equivocated his answer. I am afraid he was more concerned with the rest of the class who is suffering with the chapter in general.
Any help will be very appreaciated!