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JAMB Mathematics 1985 Question 17

Question 17

Algebraic Expressions

The factors of 9 − (x2 − 3x − 1)2 are

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

Answer: A (−(x − 4)(x + 1)(x − 1)(x − 2))

Explanation

Difference of two squares: (3 − x² + 3x + 1)(3 + x² − 3x − 1) = −(x² − 3x − 4)(x² − 3x + 2) = −(x − 4)(x + 1)(x − 1)(x − 2).