Edexcel IGCSE Maths 复习笔记 2.4.2 Factorising Quadratics - Harder

Edexcel IGCSE Maths 复习笔记 2.4.2 Factorising Quadratics - Harder

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!

Factorising a 3 term quadratic expression (a ≠ 1)

  • Signs in quadratic determine signs in brackets:
    • If c is positive then both signs are the same as the sign of b
    • If c is negative then the signs are different and bigger number has the sign of b

     

  • Using those signs find numbers p and q which
    • Multiply to give a × c
    • Add to give b
    • Cheat by writing brackets as (ax + p)(ax + q) – Yes, I know! This is not correct!
    • Uncheat by cancelling common factors in each bracket

     

Exam Tip

Check for a common factor – life will be a lot easier if you take it out before you try to factorise.If a is negative take out out a factor of -1 – that will help, too.

Worked Example

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