What is Factorisation?
Factorisation (or factoring) is the process of writing an algebraic expression as a product of two or more simpler expressions (factors). It is the reverse of multiplication.
What is Factorisation by Taking Out Common Factors?
When all terms in an expression share a common factor (number, variable, or both), we can "take it out" (factor it out) to simplify the expression.
Steps for Common Factor Method:
- Find the greatest common factor (GCF) of all terms
- Write the expression as: GCF × (remaining expression)
- Check by multiplying back
Example: 6x² + 9x
- GCF of 6x² and 9x is 3x
- 6x² + 9x = 3x(2x + 3)
What is Factorisation by Grouping Terms?
When there is no common factor in all terms, we can group terms that have common factors, then factor each group separately, and finally factor out the common binomial.
Steps for Grouping Method (for 4 terms):
- Group the terms into two pairs
- Factor out the common factor from each pair
- Look for a common binomial factor
- Factor out the common binomial