Factorising-Harder-Quadratics Aqa Higher

Factorising harder quadratics

How do I factorise a quadratic expression where a ≠ 1 in ax² + bx + c?

Method 1: Factorising by grouping

• This is shown most easily through an example: factorising 

• We need a pair of numbers that, for 

  • both multiply to give ac

    • ac in this case is 4 × -21 = -84

  • and both add to give b

    • b in this case is -25

  • -28 and +3 satisfy these conditions

  • Rewrite the middle term using -28x and +3x

    • 

  • Group and fully factorise the first two terms, using 4x as the common factor

  • and group and fully factorise the last two terms, using 3 as the common factor

    • 

  • These terms now have a common factor of <img alt=”open parentheses x minus 7 close parentheses” data-mathml=”<math ><semantics><mfenced><mrow><mi>x</mi><mo>-l