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WAEC Further Mathematics 2026 Question 20

Question 20

Binomial Theorem

Find the coefficient of x3 in the binomial expansion of [½(3 + x)]5.

  1. A.25/16
  2. B.35/16
  3. C.45/16
  4. D.55/16
Show the answer and explanation

Answer: C (45/16)

Explanation

[½(3 + x)]⁵ = (1/32)(3 + x)⁵. The x³ term of (3 + x)⁵ is ⁵C₃ × 3² x³ = 90x³, so the coefficient is 90/32 = 45/16.