Answer:
f(x) = (x + 3)(x + 1)(x - 1)x
Step-by-step explanation:
If a polynomial function has zeros at a, b, c, and d, then the polynomial is
(x - a)(x - b)(x - c)(x - d).
Here we are given that
f(-3) = 0
f(-1) = 0
f(0) = 0
f(1) = 0
That means that -3, -1, 0, and 1 are zeros of the function.
The polynomial is
(x - (-3))(x - (-1))(x - 0)(x - 1) =
= (x + 3)(x + 1)(x - 1)x
