What is a 'zero of multiplicity'?
I looked up this definition on Mathwords.com:
How many times a particular number is a zero for a given polynomial. For example, in the polynomial function $f(x) = (x – 3)^4(x – 5)(x – 8)^2$, the zero 3 has multiplicity 4, 5 has multiplicity 1, and 8 has multiplicity 2. Although this polynomial has only three zeros, we say that it has seven zeros counting multiplicity.
What is a 'zero of multiplicity' and where do the "seven zeros" come from (I know the "7" comes from adding the three exponents, "4", the hidden "1", and "2" in the equation, but why call them zeroes?)?
As in, I don't understand where the zero part of the term comes in...
(bold emphasis mine).