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JAMB 1984 · UME · Q16

Factorise 6x2−14x−126x^2 - 14x - 12.

Worked solution (try it first)
  1. Take out the common factor 2: 6x2−14x−12=2(3x2−7x−6)6x^2 - 14x - 12 = 2(3x^2 - 7x - 6).
  2. For 3x2−7x−63x^2 - 7x - 6, find two numbers with product 3×(−6)=−183 \times (-6) = -18 and sum −7-7: they are −9-9 and 2.
  3. Split the middle term and group: 3x2−9x+2x−6=3x(x−3)+2(x−3)3x^2 - 9x + 2x - 6 = 3x(x - 3) + 2(x - 3)
    =(x−3)(3x+2)= (x - 3)(3x + 2).
  4. So 6x2−14x−12=2(x−3)(3x+2)6x^2 - 14x - 12 = 2(x - 3)(3x + 2), option C.

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