Final answer:
If the 100th derivative of a polynomial function is zero, then the 98th derivative must be a constant because the original polynomial would be of degree 99 at most.
Step-by-step explanation:
If the 100th derivative of a polynomial function is zero, that means the polynomial function does not have any terms with a degree of 100 or higher. Since the derivative of a polynomial function reduces the degree of each term by one, a polynomial that ceases to exist after the 100th derivative must be of degree 99 at the highest. Therefore, the 98th derivative of such a polynomial would be a constant, as it is the result of differentiating a polynomial term of degree 99 exactly 98 times.