Study Notes
Factorisation involves rewriting an algebraic expression by taking out common factors, which is the opposite of expansion.
- Common Factor — a number or variable that divides each term in an expression Example: In 6x² + 2xy - 8xz, 2x is a common factor.
- Expansion — multiplying out brackets to simplify an expression Example: 2x(3x + y - 4z) becomes 6x² + 2xy - 8xz.
- Highest Common Factor (HCF) — the largest factor shared by all terms in an expression Example: In 8x²y + 6xy², the HCF is 2xy.
- Factorising Quadratics — finding two numbers that multiply to give the constant term and add to give the coefficient of the linear term Example: x² + 11x + 24 = (x+3)(x+8).
Exam Tips
Key Definitions to Remember
- Factorisation is the process of taking out common factors from an expression.
- Expansion is the process of multiplying out brackets.
Common Confusions
- Forgetting to take out the HCF when factorising.
- Mixing up factorisation and expansion processes.
Typical Exam Questions
- How do you factorise 36x + 24x? Answer: 12x(3 + 2)
- How do you factorise 32pq - 4pq? Answer: 4pq(8 - 1)
- How do you factorise x² + 11x + 24? Answer: (x+3)(x+8)
What Examiners Usually Test
- Ability to identify and factor out the HCF from expressions.
- Correctly factorising quadratic expressions.
- Understanding the difference between factorisation and expansion.