Final answer:
To find the zeros of the polynomial, set it equal to zero and solve for x. The zeros are x = 0, x = 19, and x = 19.
Step-by-step explanation:
To find the zeros of the given polynomial f(x) = x³ - 38x² + 361x, we set the polynomial equal to zero:
x³ - 38x² + 361x = 0
Next, we factor the polynomial:
x(x² - 38x + 361) = 0
Now, we can solve for the zeros by setting each factor equal to zero:
x = 0 (from x = 0)
x² - 38x + 361 = 0
We can either factor the quadratic or use the quadratic formula to solve for x. After solving, we find that the zeros of the polynomial are x = 0, x = 19, and x = 19.