Edexcel IGCSE Maths 复习笔记 2.4.4 Factorising Quadratics - General

Edexcel IGCSE Maths 复习笔记 2.4.4 Factorising Quadratics - General

What is a quadratic expression?

  • A quadratic expression looks like this:ax2 + bx + c (as long as a ≠ 0)
  • Note: If there are any higher powers of x (like x3 say) then it is not a quadratic!

Does it factorise?

  • It is sensible to check before trying to factorise a quadratic that it actually does factorise!
  • A quadratic will factorise if (and only if) the discriminant (b2 – 4ac) is a perfect square
  • If it does factorise then you have to decide what to do:

Decisions, decisions…

  • Always check for a Common (numerical) Factor before you factorise – spotting it early will make life a lot easier
  • Take it out and just leave it in front of a big bracket
  • When the quadratic expression only has two terms check for:
    • Simple factorisation (no number term, ie. when c = 0 )
    • Difference Of Two Squares (no x term, ie. when b = 0)

     

  • Once you have decided that it is a factorisable three term quadratic with no common numerical factors then you can follow the normal rules (see other Notes for those!)
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