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WAEC Further Mathematics 2013 Question 25

Question 25

Polynomials

Express (x2 + x + 4)/((1 − x)(x2 + 1)) in partial fractions.

  1. A.x2/(x2 + 1) + (x + 4)/(1 − x)
  2. B.3/(1 − x) + (2x + 1)/(x2 + 1)
  3. C.x2/(1 − x) + (x + 4)/(x2 + 1)
  4. D.3/(1 − x) + (2x + 2)/(x2 + 1)
Show the answer and explanation

Answer: B (3/(1 − x) + (2x + 1)/(x2 + 1))

Explanation

Write A/(1 − x) + (Bx + C)/(x² + 1). x = 1 gives 6 = 2A, A = 3; comparing x² terms, 1 = 3 − B so B = 2; constants, 4 = 3 + C so C = 1.