Answer:
k=3
Explanation:
If x-1 is a factor of f(x), then f(1) = 0.
f(x) = x^3 - kx^2 + 2x
f(1) = (1)^3 - k(1)^2 + 2(1) = 0
Now, solve for k
(1)^3 - k(1)^2 + 2(1) = 0
1 - k + 2 = 0
-k = -3
k = 3
9514 1404 393
Using synthetic division, we see the remainder from division by (x-1) is 3-k. In order for (x-1) to be a factor, that remainder must be zero.
3 -k = 0
3 = k
The value of k is 3.
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