Question Detail
Question
The coefficients of the second and third term of the expansion of \( (1 + cx)^3 \) are 6 and 12 respectively. If c is a positive integer, find the value of c.
Correct Answer
Option B is the correct answer.
Detailed Explanation
The expansion of (1+cx)³ = 1 + 3(cx) + 3(cx)² + (cx)³ = 1 + 3c x + 3c² x² + c³ x³. The second term coefficient is 3c = 6 => c=2. The third term coefficient is 3c² = 3(4)=12, which matches. So c=2.
Hint
Use the binomial theorem for n=3 and equate coefficients.