Answer:
f(x) = -2(x + 3)(x + 1)(x - 4)(x - 1) or
f(x) = -2x^4 + 2x^3 + 26x^2 - 2x -24.
Step-by-step explanation:
The zeros of the function are at (-3, 0), (-1, 0), (4, 0), (1, 0) so in factor form the function is:
a(x + 3)(x + 1)(x - 4)(x - 1) where a is some constant.
We find a by substituting the point (2, 60)
60 = a(2+3)(2+1)(2-4)(2-1)
-30a = 60
a = -2.
So the function is -2(x + 3)(x + 1)(x - 4)(x - 1) .
