To determine k so that (x-2) is a factor of (x^4 - 2x^3 + kx + 6), we could use the fact that:
If x-2 is a factor, then x=2 is a zero.
Now, we know that a polynomial has a zero when it becomes zero, so, if we replace x=2 in the expression and the result is zero, that means that x=2 is actually a zero:
Therefore, k = -3 so that (x-2) is a factor of x^4 - 2x^3 + kx + 6