Final answer:
A zero 'c' of multiplicity 'k' implies that (x - c) appears k times as a factor in the polynomial P(x), affecting the graph's behavior at the point (c, 0).
Step-by-step explanation:
When we say that c is a zero of multiplicity k of a polynomial P, we are indicating that the polynomial function P(x) has (x - c) as a factor k times.
That is to say, the term (x - c) will appear k times in the factored form of the polynomial. For example, if a polynomial has a zero of c = 2 with a multiplicity of k = 3, then (x - 2) would be a factor of the polynomial three times, usually written as (x - 2)3 within the polynomial's factored form.
The presence of a zero of multiplicity greater than one implies that the graph of the polynomial will “touch” or be tangent to the x-axis at the point (c, 0) without crossing it if k is an even number, or it will cross the x-axis if k is an odd number.