Factorising (CIE IGCSE Maths: Core)

What is factorisation?

• A factorised expression is one written as the product (multiplication) of two, or more, terms (factors)
  • 3(x + 2) is factorised, as it is 3 × (x + 2)
  • 3x + 6  is not factorised as it is "something" + "something"
  • 3xy is factorised as it is 3 × x × y
  • 12 can also be factorised: 12 = 2 x 2 x 3
• In algebra, factorisation is the opposite of expanding brackets
  
  • it's "putting it into" brackets

How do I factorise two terms?

• To factorise 12x² + 18x  
  • The highest common factor of 12 and 18 is 6
  • The highest common factor of x² and x is x
    • this is the largest letter that divides both x² and x 
  • Multiply both to get the common factor
    • 6x
  • Rewrite each term in 12x² + 18x  as "common factor × something"
    • 6x × 2x + 6x × 3
  • "Take out" the common factor by writing it outside brackets
  • Put the remaining 2x + 3 inside the brackets
    • Answer: 6x(2x + 3)
    • Check this expands to give 12x² + 18x