Final answer:
The value of k is -9.
Step-by-step explanation:
Given f(x) = x³ + 8x + kf(x) = x³ + 8x + k, and (x - 1) is a factor of f(x), we can use synthetic division to find the value of k.
Using the factor theorem, if (x - 1) is a factor of f(x), then f(1) = 0.
Substituting x = 1 into f(x), we get:
f(1) = 1³ + 8(1) + k = 1 + 8 + k = 9 + k
Since f(1) = 0, we can solve for k:
9 + k = 0
k = -9