Final answer:
To find the value of k for f(x) when (x + 1) is a factor, we apply the Factor Theorem and find that k equals -5.
Step-by-step explanation:
To determine the value of k when given that f(x) = 2x³ - 7x + k and (x + 1) is a factor of f(x), we need to apply the Factor Theorem. The Factor Theorem states that if (x + 1) is a factor of f(x), then f(-1) = 0. Therefore, we can substitute x with -1 and solve for k.
Plugging -1 into the equation we get: 2(-1)³ - 7(-1) + k = 0. Simplifying this equation we have: -2 + 7 + k = 0, which leads to k = -5. Hence, the value of k is -5.