Question Detail
Question
Find the term independent of \( x \) in \( (2x + 1/x^2)^9 \).
Correct Answer
Option A is the correct answer.
Detailed Explanation
General term: T_{r+1} = C(9,r) (2x)^{9-r} (1/x²)^r = C(9,r) 2^{9-r} x^{9-r-2r} = C(9,r) 2^{9-r} x^{9-3r}. For term independent of x, set exponent 9-3r=0 => r=3. Coefficient = C(9,3) * 2^{6} = 84 * 64 = 5376.
Hint
Set the exponent of x to zero to find the term independent of x.