Question

What is a polynomial function in standard form with zeroes 0, 1, 4, and –1?

Answer 1

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