Introduction:
To find the value of 'k' if x-1 is a factor of p(x), we need to determine the conditions under which p(x) is divisible by x-1. In other words, we need to find the values of 'k' for which p(x) has a root at x=1.

Understanding the Problem:
We are given p(x) = x^2 - 3kx, and we need to determine the value of 'k' for which x-1 is a factor of p(x). This implies that p(1) should be equal to zero, as a factor of x-1 means that p(x) is divisible by x-1.

Solution:
Let's substitute x=1 in p(x) and set the result equal to zero:

p(1) = 1^2 - 3k(1)
0 = 1 - 3k

Now, we solve the equation to find the value of 'k':

1 - 3k = 0
3k = 1
k = 1/3

Therefore, the value of 'k' for which x-1 is a factor of p(x) is k = 1/3.

Summary:
In summary, we found that the value of 'k' for which x-1 is a factor of p(x) = x^2 - 3kx is k = 1/3. This was determined by setting p(1) equal to zero and solving for 'k'.