GCSE factoring trinomials revision
Use this page when you want the trinomial method in a revision-friendly format rather than a full algebra lesson.
Start here if you want the short version before reading the full method.
- For many GCSE trinomials, the first check is whether two numbers multiply to the constant term and add to the middle coefficient.
- If the coefficient before x^2 is not 1, the ac method or grouping route is often the safer revision pattern.
What this topic means and what to look for first.
This page is meant for quick revision: recognise the pattern, work one clean example, and then test yourself on a short set.
It works best as a recap page before practice or before using a solver on a specific problem.
One reliable route through the topic.
- 1Put the trinomial into standard form if needed.
- 2Check whether the first coefficient is 1 or not.
- 3Choose the matching route: factor-pair search or ac method.
- 4Write the brackets carefully and expand to verify.
- 5Use a short answer check before moving to the next question.
Choose the route that fits the quadratic.
Best for standard GCSE bracket questions such as x^2 + 5x + 6.
Useful when the coefficient before x^2 is not 1 and guessing becomes unreliable.
See the method in action.
x^2 + 7x + 12
- Look for two numbers that multiply to 12 and add to 7.
- The pair is 3 and 4.
- So the factorisation is (x + 3)(x + 4).
x^2 - x - 12
- Look for two numbers that multiply to -12 and add to -1.
- The pair is -4 and 3.
- So the factorisation is (x - 4)(x + 3).
2x^2 + 7x + 3
- Use ac = 6 and split the middle term as 6x and x.
- Group and factor to get (2x + 1)(x + 3).
- Expand to check that the middle term returns as 7x.
Things that commonly send the method off track.
- Choosing a factor pair too quickly without checking the middle term.
- Missing the sign pattern when the constant is negative.
- Treating a non-1 coefficient question as if it were the easy bracket case.
Use a short verification pass before moving on.
- Expand the brackets after every practice question until the check feels automatic.
- If the constant matches but the middle term does not, pause and revise the factor pair.
Try a few variations before switching to a calculator or solver tool.
- x^2 + 9x + 20
- x^2 - 2x - 15
- 2x^2 + 9x + 10
- 3x^2 + 11x + 6
Want to try a similar problem yourself?
Create a free account if you want to use the solver beta after reading the guide.
A free account is the current follow-up route for returning to the solver beta and future guide updates as the public library grows.
Extra factorising practice resources
These options are a sensible follow-up if you want more factorising practice beyond this page.
Amazon
Factorising quadratics and trinomials revision books
Useful when you want more bracket practice, sign practice, and mixed quadratic factorisation examples.
View Factorising quadratics and trinomials revision booksAmazon
GCSE algebra factorising workbook search
A wider algebra-workbook route if you want factorising alongside equations and related revision topics.
View GCSE algebra factorising workbook searchNeed live help with factorising?
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Short answers worth checking.
Focus on the two main patterns: standard a = 1 bracket questions and the ac method for cases where the first coefficient is not 1.
Check whether the expression starts with x^2 or with a larger coefficient, because that usually decides which method is fastest.
Continue with the next closely related topic.
Use the public site structure first, then switch into the solver tool only if you need a direct test.
CureMath uses artificial intelligence to suggest how a maths problem could potentially be solved. AI can make mistakes.
Check important answers independently before relying on them.