Watch out
Stopping after only a common factor when more factorisation is possible.
Scottish National 5 Mathematics
National 5 Maths Factorising
Factorise common factors, difference of squares and unitary or non-unitary trinomials.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Check for a common factor first.
- Be ready to work exactly without a calculator and show each mathematical step.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Factorising is an assessed part of Scottish National 5 Mathematics in the algebra area. Factorise common factors, difference of squares and unitary or non-unitary trinomials.
Check for a common factor first.
Identify the factor pair whose product and sum match the expression.
Expand the factors to verify the middle term.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- a² − b² = (a − b)(a + b)
Check
Expand, factorise or substitute back into the original expression to verify the result.
Exam tip
Keep equations aligned line by line so method marks remain visible, especially through sign and bracket changes.
Worked examples
Worked example 1
Factorising worked example
Factorise 6x² + 11x + 3
- 6 × 3 = 18; the matching pair is 9 and 2
- 6x² + 9x + 2x + 3 = 3x(2x + 3) + 1(2x + 3)
Answer: (3x + 1)(2x + 3)
Watch out
- Stopping after only a common factor when more factorisation is possible.
- Not checking a non-unitary middle term.