Factorising (Edexcel GCSE Maths): Revision Notes
Factorising
Factorising is the reverse process of expanding brackets. When you factorise an expression, you take out the largest common factor from all terms and write it outside brackets.
What is factorising?
Factorising means finding the largest factor that divides into every term of an expression. This factor is written outside brackets, with the remaining terms placed inside.
Basic Example: Factorising vs Expanding
For the expression :
- Expanding:
- Factorising:
The factorising process
Factorising can seem complex at first, but following a systematic approach makes it much more manageable. The key is to work through each step methodically and always check your final answer.
The 4-Step Factorising Method
Step 1: Look for the largest factor you can take out of every term
- Example: In , the largest factor is
Step 2: Write this factor outside brackets, including the correct sign (+ or -)
- Example:
Step 3: Work out what you need to multiply the factor by to get each term in the original expression
- Example: , and
- So:
Step 4: Check your answer by expanding the brackets
- Example: and ✓
Complete vs partial factorising
Understanding the difference between complete and partial factorising is crucial for achieving the highest marks in examinations.
Partial factorising
Taking out only some common factors, leaving more that could be removed.
Example of Partial Factorising
This has only been partly factorised because is not the largest possible factor.
Complete factorising
Taking out the largest possible common factor from all terms.
Always aim for complete factorisation!
Example:
This is completely factorised because is the largest factor common to both terms.
Worked examples
Basic factorising (Target Grade 3-4)
Worked Example: Simple Variable Factorising
Question: Factorise
Solution:
- Common factor:
- Answer:
- Check: and ✓
Factorising with coefficients (Target Grade 4-5)
Worked Example: Factorising with Coefficients
Question: Factorise
Solution:
- Common factor:
- Answer:
- Check: and ✓
Exam guidance
Essential Exam Tips
- Always look for the largest common factor - don't settle for partial factorising
- Check your answer by expanding the brackets back to the original expression
- Watch out for signs - negative terms need careful handling when factorising
- Both parts inside and outside brackets are factors of the original expression
Key Points to Remember:
- Factorising is the opposite of expanding brackets
- Always find the largest common factor to avoid partial factorising
- Use the 4-step process: find factor → write outside brackets → work out inside terms → check by expanding
- Check your answer by multiplying out the brackets
- Include correct signs when factorising expressions with negative terms