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WAEC Further Mathematics 2026 Question 9

Question 9

Polynomials

Given that (2x + 3)/(x2 − 3x + 2) ≡ A/(x − 1) + B/(x − 2), find the values of A and B.

  1. A.A = −5, B = 7
  2. B.A = 5, B = −7
  3. C.A = −5, B = −7
  4. D.A = 5, B = 7
Show the answer and explanation

Answer: A (A = −5, B = 7)

Explanation

x² − 3x + 2 = (x − 1)(x − 2), so 2x + 3 = A(x − 2) + B(x − 1). Put x = 1: 5 = −A, so A = −5. Put x = 2: 7 = B. Check: −5(x − 2) + 7(x − 1) = 2x + 3.