Watch out
Choosing a method from a remembered keyword instead of reading the whole question.
Back to National 5 Mathematics
SQA National 5 Mathematics
Factorising
Taking out common factors and recognising useful factorisations.
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
- Read the command word and identify what is being asked.
- Write down the relevant formula, rule or algebraic structure before substituting values.
- Keep working set out line by line so method marks are clear.
Explanation
Factorising is part of Number and Algebra in SQA National 5 Mathematics. The key skill is choosing a method and communicating the working clearly.
For factorising, underline the values or algebraic terms you are given, choose the matching rule, then simplify one line at a time.
National 5 answers should show enough working for a marker to follow the method. Exact answers are expected where the question asks for exact form; otherwise round only at the end.
Key formulae and rules
- Mostly non-calculator algebra.
Check
Compare your answer with the size you expected from the question.
Exam tip
Method marks come from clear setup and correct mathematical notation, not just a final answer.
Calculator tip
Use brackets for fractions, powers and square roots, then round only at the final line.
Worked examples
Worked example 1
Simplify an expression
Simplify 3x + 4x − 2.
- Collect like terms: 3x + 4x = 7x
- Keep the constant term −2.
Answer: 7x − 2.
Worked example 2
Solve an equation
Solve 5x − 7 = 18.
- Add 7 to both sides: 5x = 25
- Divide by 5.
So: x = 5
Worked example 3
Check the answer
Check x = 5 in 5x − 7 = 18
- 5(5) − 7 = 25 − 7
- 25 − 7 = 18
Answer: The solution checks correctly.
Watch out
- Choosing a method from a remembered keyword instead of reading the whole question.
- Dropping negative signs, powers or brackets during the working.
- Giving a rounded decimal when an exact answer or algebraic form is needed.