GCSE Maths (AQA)

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Advanced Quadratics - Splitting Method

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Algebra Notation, Vocabulary and Manipulation

Advanced Quadratics - Splitting Method

6:21 Factorisation
Spec A1 A4
Previous Advanced Quadratics - Inspection Method Next Advanced Changing the Subject
  • Some quadratics with coefficients of X squared greater than one can be factorized using the splitting method
  • The linear X term is split into two added terms
  • The coefficients of these terms need to multiply together to give the same number obtained from multiplying the coefficient of the X squared term and the constant term
  • The split terms need to multiply together to give the product of the X squared coefficient and the constant term
  • Quadratics with coefficients of X squared greater than 1 can also be factorized using inspection
  • Example: Factorize 2x squared plus 11x plus 15
  • Step 1: Find the product of the X squared coefficient and the constant term (2 times 15 = 30)
  • Step 2: Split the X term into two terms that multiply to the previous product (6x and 5x)
  • Step 3: Factorize the first two terms (2x squared plus 6x)
  • Step 4: Factorize the last two terms (5x plus 15)
  • Step 5: Factorize again, taking the bracket as a common factor (x plus 3 times 2x plus 5)
  • Another example: Factorize 3x squared minus 16x minus 12
  • Step 1: Find the product of the X squared coefficient and the constant term (3 times -12 = -36)
  • Step 2: Split the X term into two terms that multiply to the previous product (-18x and 2x)
  • Step 3: Factorize the first two terms (3x times x minus 6)
  • Step 4: Factorize the last two terms (2x minus 6)
  • Step 5: Factorize again, taking the bracket as a common factor (x minus 6 times 3x plus 2)

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