Final answer:
The x-intercepts of the function f(x) = x^3 + 4x^2 - 11x - 30 are -6, 1, and -5.
Step-by-step explanation:
The x-intercepts of a function are the points where the graph of the function intersects the x-axis. To find the x-intercepts of the function f(x) = x^3 + 4x^2 - 11x - 30, we set the function equal to zero and solve for x.
Using synthetic division or factoring, we can find that the function can be factored as f(x) = (x + 6)(x - 1)(x + 5). Hence, the x-intercepts are x = -6, x = 1, and x = -5.