Answer:
The polynomial function can be written as:
f(x) = (x + 5)(x - 2)(x - 8)
This polynomial function will have zeros at x = -5, 2, and 8, and will have no other zeros.
Explanation:
A polynomial function has zeros at x = -5, 2, 8 if and only if the polynomial can be written in the form (x + 5)(x - 2)(x - 8) = 0.
The general form of a polynomial function is:
f(x) = ax^n + bx^(n-1) + cx^(n-2) + ... + dx + e
where n is the degree of the polynomial and a, b, c, ..., d, e are constants.
For the polynomial function with zeros at x = -5, 2, 8, the degree is 3 (since there are 3 distinct zeros) and the constants are a = 1, b = 0, c = 0, d = 0, and e = 0.