Answer:
The answer is:
f(x) = -4x^3 + 52x + 48
Explanation:
Since the polynomial has zeros at -3, -1, and 4, it can be written in the form:
f(x) = a(x + 3)(x + 1)(x - 4)
where a is a real coefficient.
We are given that f(−2)=−24. Substituting x=−2 into the above equation, we get:
-24 = a(-2 + 3)(-2 + 1)(-2 - 4)
Simplifying both sides, we get a=−4.
Therefore, the polynomial function we are looking for is:
f(x) = -4(x + 3)(x + 1)(x - 4)
This can also be written in standard form as:
f(x) = -4x^3 + 52x + 48