Quadratics Factorising Methods (AQA GCSE Maths)

How do I know if it factorises?

• Method 1: Use a calculator to solve the quadratic expression equal to 0
  • If the solutions are integers or fractions (without square roots), then the quadratic expression factorises
• Method 2: Find the value under the square root in the quadratic formula, b² – 4ac (called the discriminant)
  • If this number is a perfect square number, then the quadratic expression factorises

Which factorisation method should I use for a quadratic expression?

• Does it have 2 terms only?
  • Yes, like 
    • Use "basic factorisation" to take out the highest common factor
    • 
  • Yes, like 
    • Use the "difference of two squares" to factorise
    • 
• Does it have 3 terms?
  • Yes, starting with x² like
    • Use "factorising simple quadratics" by finding two numbers that add to -3 and multiply to -10
    • 
  • Yes, starting with ax² like
    • Check to see if the 3 in front of x² is a common factor for all three terms (which it is in this case), then use "basic factorisation" to factorise it out first
    • 
    • The quadratic expression inside the brackets is now x² +... , which factorises more easily
    • 
  • Yes, starting with ax² like
    • The 3 in front of x² is not a common factor for all three term
    • Use "factorising harder quadratics", for example factorising by grouping or factorising using a grid
    •