Final answer:
To find the value of k such that x - 3 is a factor of p(x), substitute x with 3 in p(x) and set it equal to 0. Combine like terms and solve for k to find the value.
Step-by-step explanation:
To find the value of k such that x - 3 is a factor of p(x), we need to use the Remainder Theorem. According to the theorem, if x - 3 is a factor of p(x), then p(3) should be equal to 0. So, substitute x with 3 in p(x) and set it equal to 0:
2(3)^3 + k(3)^2 - k(3) + 6 = 0
54 + 9k - 3k + 6 = 0
9k - 3k + 60 = 0
Combine like terms:
6k + 60 = 0
Subtract 60 from both sides:
6k = -60
Divide by 6:
k = -10