Question Detail
Question
Find the coefficient of \(x^{-12}\) in \((x^3 - 1/x)^{24}\).
Correct Answer
Option B is the correct answer.
Detailed Explanation
General term: T_{r+1} = C(24,r) (x^3)^{24-r} (-1/x)^r = C(24,r) (-1)^r x^{72-3r} x^{-r} = C(24,r) (-1)^r x^{72-4r}. Set exponent = -12: 72 - 4r = -12 ⇒ 4r = 84 ⇒ r = 21. Coefficient = C(24,21) (-1)^21 = C(24,3) (-1) = 2024 × (-1) = -2024.
Hint
Use the general term formula and set the exponent of x to the required value.