Final answer:
The zeros of a polynomial that occur an even number of times are those with an even multiplicity, which is indicated by factors in the polynomial with even exponents.
Step-by-step explanation:
To determine which zero(s) of a polynomial function occur an even amount of times, we need to look at the multiplicity of the zeros. A zero of multiplicity 2 or any even number will occur an even amount of times. Let's consider an example:
If the polynomial function is f(x) = (x - 2)^3 (x + 1)^2 (x - 3), the zeros are 2, -1, and 3. The zero 2 has a multiplicity of 3 (odd), -1 has a multiplicity of 2 (even), and 3 has a multiplicity of 1 (odd). Therefore, the zero -1 occurs an even amount of times.