To find the zeros of the function f(x) = x^3 - 4x^2 - 32x, we set the function equal to zero and solve for x. The zeros of the function are x = 0, x = -4, and x = 8.
Step-by-step explanation:
The given function is f(x) = x^3 - 4x^2 - 32x. To find the zeros of the function, we set f(x) equal to zero and solve for x.
x^3 - 4x^2 - 32x = 0
Next, we can factor out an x from the equation:
x(x^2 - 4x - 32) = 0
We can now solve for x by setting each factor equal to zero:
x = 0
x^2 - 4x - 32 = 0
Using the quadratic formula, we find that the solutions to x^2 - 4x - 32 = 0 are x = -4 and x = 8.
Therefore, the zeros of the function f(x) = x^3 - 4x^2 - 32x are x = 0, x = -4, and x = 8.