Minimum Number of Zeroes in a Polynomial Function

On a previous math test, we had the following question:

Given f(x) is a polynomial of degree 3, then f has at least ____ zero(s) in the complex number system.

My teacher is saying that due to the Linear Factorization Theorem, which states for a polynomial function f of degree n, f has precisely n linear factors, that the answer is 3.

I however, think that the answer is 1, according the the fundamental theorem of algebra.

To provide an example, I used the equation x3 = 0. The function can be factored into three linear factors, x * x * x = 0, but that does not mean that it has 3 complex zeroes; it has 1, which is 0.

My teacher is arguing that the due to multiplicity, the 0 counts three times - but given the context of the problem, I don't think that this is true.

Who is correct?