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JAMB 1985 · UME · Q17

The factors of 9−(x2−3x−1)29 - (x^2 - 3x - 1)^2 are

Worked solution (try it first)
  1. This is a difference of two squares, with 9=329 = 3^2: 32−(x2−3x−1)2=(3−x2+3x+1)(3+x2−3x−1)3^2 - (x^2 - 3x - 1)^2 = (3 - x^2 + 3x + 1)(3 + x^2 - 3x - 1).
  2. Tidy each bracket: (4+3x−x2)(x2−3x+2)(4 + 3x - x^2)(x^2 - 3x + 2).
  3. Factorise: 4+3x−x2=−(x2−3x−4)4 + 3x - x^2 = -(x^2 - 3x - 4)
    =−(x−4)(x+1)= -(x - 4)(x + 1), and x2−3x+2=(x−1)(x−2)x^2 - 3x + 2 = (x - 1)(x - 2).
  4. So the factors are −(x−4)(x+1)(x−1)(x−2)-(x - 4)(x + 1)(x - 1)(x - 2), option A.

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