Factorising Harder Quadratics: ax² + bx + c (GCSE Higher)

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About Course

Factorise quadratic expressions where the x² term has a coefficient other than 1, such as 6x² + 11x + 3, and use this to solve equations and simplify algebraic fractions. This is Higher tier GCSE content, explained step by step with fully checked worked examples.

Tutwoo is an independent learning provider. This course supports revision for GCSE Mathematics (Higher tier) in England. It is not produced or endorsed by any exam board and is not an accredited qualification.

© 2026 Tutwoo UK Limited. This course was created in-house by Tutwoo and is our original work. It is for your own learning only: please do not copy, share, record or resell it.

What Will You Learn?

  • Spot and remove a common factor before anything else
  • Factorise ax² + bx + c by splitting the middle term
  • Use difference of two squares and sign patterns to work faster
  • Solve quadratic equations and simplify algebraic fractions by factorising

Course Content

Course Lessons

  • Why a ≠ 1 is different
  • Splitting the middle term
  • Sign patterns, trial and difference of two squares
  • Solving equations and simplifying fractions

Sources & Further Reading
The official guidance this course is based on.

Final Assessment

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