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The factors of 9 - (x2 - 3x - 1)2 are

Mathematics
JAMB 1985

The factors of 9 - (x2 - 3x - 1)2 are
  • A. -(x - 4)(x + 1) (x - 1)(x - 2)
  • B. (x - 4)(x - 2) (x - 1)(x + 1)
  • C. -(x - 2)(x + 1) (x - 2) (x - 1)
  • D. (x - 2)(x + 2) (x - 1)(x + 1)
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Correct Answer: Option A
Explanation
9 - (x2 - 3x - 1)2 = [3 - (x2 - 3x - 1)] [3 + (x2 - 3x - 1)]

= (3 - x2 + 3x + 1)(3 + x2 - 3x - 1)

= (4 + 3x - x2)(x2 - 3x + 2)

= (4 - x)(1 + x)(x - 1)(x - 2)

= -(x - 4)(x + 1) (x - 1)(x - 2)

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