Final answer:
To find the value of k so that x-1 is a factor of the polynomial 2x³-18x+k, we use the remainder theorem and substitute x=1 into the polynomial, which gives us the value of k as 16.
Step-by-step explanation:
To find the value of k so that x-1 is a factor of 2x³-18x+k, we use the remainder theorem which states that for a polynomial f(x), if x-c is a factor, then f(c) = 0. Since we know that x-1 is a factor, we can substitute x=1 into the polynomial and set it equal to zero to solve for k.
Let's substitute x = 1 into the polynomial:
- 2(1)³ - 18(1) + k = 0
- 2 - 18 + k = 0
- k = 16
Therefore, the value of k is 16 for x-1 to be a factor of 2x³-18x+k.