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JAMB Mathematics 1989 Question 20

Question 20

Algebraic Expressions

If one factor of x3 − 8−1 is x − 2−1 the other factor is

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

Answer: D (x2 + 2−1x + 4−1)

Explanation

This is a difference of cubes: x³ − (½)³ = (x − ½)(x² + ½x + ¼).