Study Notes
Factorisation involves expressing an expression as a product of its factors, which is the opposite of expansion.
- Common Factor — taking out the greatest common factor from terms. Example: 8x^2y + 6xy^2 = 2xy(4x + 3y)
- Factorising Quadratics — finding two numbers that multiply to give the product of the quadratic term's coefficient and the constant, and add to give the linear term's coefficient. Example: x^2 + 11x + 24 = (x+3)(x+8)
- Difference of Two Squares — a method for factorising expressions in the form a^2 - b^2. Example: x^2 - 16 = (x+4)(x-4)
Exam Tips
Key Definitions to Remember
- Factorisation is the process of expressing an expression as a product of its factors.
- Difference of Two Squares is a^2 - b^2 = (a+b)(a-b).
Common Confusions
- Forgetting to take out the greatest common factor first.
- Mixing up the signs when using the difference of two squares.
Typical Exam Questions
- How do you factorise 2x^2 - 4x - 6? Answer: 2(x+1)(x-3)
- What is the factorised form of x^2 - 16? Answer: (x+4)(x-4)
- How do you factorise x^2 + 11x + 24? Answer: (x+3)(x+8)
What Examiners Usually Test
- Ability to identify and factor out the greatest common factor.
- Correct application of the difference of two squares.
- Factorisation of quadratic expressions with and without a leading coefficient.