The Solution:
Given the polynomial below:

It is given that (x - 2) is a factor of f(x).
We are required to find all the zeros of f(x) using the Factor Theorem.
Step 1:
Recall:
The Factor Theorem states that:
If we divide a polynomial f(x) by (x - c), and (x - c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0.
So, we shall divide f(x) by (x - 2), and equate the result to zero.
![\begin{gathered} \text{ x}^2-6x+5 \\ (x-2)\sqrt[]{x^3-8x^2+17x-10} \\ \text{ -(x}^3-2x^2) \\ ---------------- \\ \text{ -6x}^2+17x-10 \\ \text{-(-6x}^2+12x) \\ ---------------- \\ \text{ +5x-10} \\ \text{ -(}5x-10) \\ ----------------- \\ \text{ 0} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/2743uaq2fvsyte9k42ybrqio6dpyyjbslw.png)
It follows by the Factor Theorem that:

Solving the above quadratic equation by the Factorization Method, we get

So, we have that:

Similarly,

So, the zeros of f(x) are: 2,1,5
Therefore, the correct answers are:
