Deciding the Factorisation Method (Cambridge (CIE) IGCSE International Maths)

Quadratics Factorising Methods

How do I know if an expression factorises?

• The easiest way to check if ax² + bx + c factorises is to check if you can find a pair of integers which:

  • Multiply to give ac

  • Sum to give b

  • If you can find integers to satisfy this, the expression must factorise

• There are some alternate methods to check:

  • Method 1: Use a calculator to solve the quadratic expression equal to 0

    • Only some calculators have this functionality

    • If the solutions are integers or fractions (without square roots), then the quadratic expression will factorise

  • Method 2: Find the value under the square root in the quadratic formula

    • b² – 4ac

    • If this number is a square number, then the quadratic expression will factorise

Which factorisation method should I use for a quadratic expression?

• Does it have 2 terms only?

  • Yes, like 

    • Factorise out the highest common factor, x

    • 

  • 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 factorise it out of all three terms

  • 

  • 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

  • 

What other expressions should I be able to factorise?

• You may have a cubed term like

  • Check to see if x is a common factor for all three terms (which it is in this case), so factorise it out of all three terms

  • 

  • The remaining quadratic can then be factorised

  • 

• It can also be useful to spot a quadratic in the form

  • This factorises to

  • E.g.