The polynomial for this case is given by: (x) * (x-1) * (x + 1) * (x-4) = 0 Rescribing we have: (x) * (x ^ 2-1) * (x-4) = 0 (x) * (x ^ 3 - 4x ^ 2 - x + 4) = 0 (x ^ 4 - 4x ^ 3 - x ^ 2 + 4x) = 0 Therefore, the polynomial in standard form is: f (x) = x ^ 4 - 4x ^ 3 - x ^ 2 + 4x Answer: a polynomial function in standard form with zeroes 0, 1, 4, and -1 is: f (x) = x ^ 4 - 4x ^ 3 - x ^ 2 + 4x
