Step-by-step Solution:

Explanation:

We are given that (x - 1) is a factor of: \[ 2x^2 - 5x + k = 0 \]

By the Factor Theorem, if (x - 1) is a factor, then substituting \(x = 1\) into the polynomial must make it equal to 0.

\[ P(x) = 2x^2 - 5x + k \] \[ P(1) = 2(1)^2 - 5(1) + k = 0 \]

Simplify: \[ 2 - 5 + k = 0 \] \[ -3 + k = 0 \quad \Rightarrow \quad k = 3 \]

Hence, the correct value of \(k\) is:

(C) 3