Answer: The zeros of the polynomial function F(x) = x³ - x² - 6x are 0, 2, and -3.
Explanation:
The zeros of a polynomial function are the values of x that make the function equal to zero. To find the zeros of the function F(x) = x³ - x² - 6x, we can set the function equal to zero and solve for x:
x³ - x² - 6x = 0
One way to solve for x is to factor the polynomial:
x(x² - x - 6) = 0
This gives us three possible values for x: x = 0, x = 2, and x = -3. To verify that these are indeed the zeros of the function, we can substitute each value back into the original equation and see if it equals zero.
Therefore, the zeros of the polynomial function F(x) = x³ - x² - 6x are 0, 2, and -3.