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JAMB Mathematics 1999 Question 19

Question 19

Polynomials

Express 1/(x3 − 1) in partial fractions.

  1. A.⅓(1/(x − 1) − (x − 2)/(x2 − x + 1))
  2. B.⅓(1/(x − 1) − (x + 2)/(x2 + x + 1))
  3. C.⅓(1/(x − 1) − (x − 2)/(x2 + x + 1))
  4. D.⅓(1/(x − 1) − (x + 2)/(x2 − x − 1))
Show the answer and explanation

Answer: B (⅓(1/(x − 1) − (x + 2)/(x2 + x + 1)))

Explanation

x³ − 1 = (x − 1)(x² + x + 1). Write 1 = A(x² + x + 1) + (Bx + C)(x − 1): x = 1 gives A = 1/3, then B = −1/3 and C = −2/3.