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!)