Final answer:
The zeros of the polynomial f(x) = x^3 - x^2 + 25x - 25 are x = 1 and two complex roots.
Step-by-step explanation:
The given polynomial is f(x) = x^3 - x^2 + 25x - 25.
We are given that (x-1) is a factor of the polynomial, so we can use synthetic division to find the other two roots.
Using synthetic division, we divide (x-1) into the polynomial to get the quotient x^2 + 0x + 25. This gives us the equation (x-1)(x^2 + 0x + 25) = 0.
To find the zeros of the quadratic equation x^2 + 0x + 25 = 0, we can use the quadratic formula. The discriminant is b^2 - 4ac = 0^2 - 4(1)(25) = -100. Since the discriminant is negative, the quadratic equation has no real solutions. Therefore, the zeros of the polynomial f(x) = x^3 - x^2 + 25x - 25 are x = 1 and two complex roots.