Factorising Quadratics (Edexcel IGCSE Further Pure Maths)

Factorising Quadratics

How can I factorise simple quadratics?

• If there is no constant term then just factorise out (a multiple of) 

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• Factorise quadratics of the form  by inspection

  • Find a pair of numbers,  and , that multiply to give and add to give 

    • E.g. for  the numbers would be  and 

  • The quadratic will factorise as 

    • So   

How can I factorise harder quadratics?

• A harder quadratic is of the form  where  is not equal to 1 (or 0)

  • E.g. 

• These can also be factorised by inspection

  • This requires a lot of practice and there are no simple rules to follow

• They can be factorised reliably by grouping

  • Find a pair of numbers that multiply to and add to 

    • For ,   and 

    • So the two numbers are  and 

  • Rewrite the middle  term using those two numbers

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  • Group and factorise the first two terms and the last two terms by pulling out common factors

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  • Those two terms now have a common factor (in brackets) that can be factorised out

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How do I factorise a difference of two squares

• A difference of two squares refers to any expression of the form 

  • I.e. 'something squared subtracted from something else squared'

  • For example,

    • 

    • 

    • 

    •   which is equal to  

• Such expressions will factorise as 

  • This is because  

  • So

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    •   which is equal to

    • which is equal to 

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