Solution

Given: Polynomial $$f(x) = 2x^2 - 5x + k$$ and $(x-1)$ is a factor.

Step 1: Apply factor theorem.
If $(x-1)$ is a factor, then $f(1) = 0$.

Step 2: Substitute $x=1$.
$$f(1) = 2(1)^2 - 5(1) + k = 2 - 5 + k = -3 + k$$

Step 3: Solve for $k$.
$$-3 + k = 0 \quad \Rightarrow \quad k = 3$$

Value of k: 3

Answer: Option 3