Study Notes
Factorisation is the process of 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)
- Factorisation of Quadratics — finding two numbers that multiply to give the product of the quadratic term's coefficient and the constant term, and add to give the linear term's coefficient. Example: x^2 + 11x + 24 = (x+3)(x+8)
- Difference of Two Squares — expressing a difference of squares as a product of a sum and difference. Example: x^2 - 16 = (x+4)(x-4)
Exam Tips
Key Definitions to Remember
- Factorisation is the opposite of expansion.
- Difference of Two Squares: 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 squares.
Typical Exam Questions
- How do you factorise 6x^2 + x - 2? (2x-1)(3x+2)
- What is the factorisation of x^2 - 16? (x+4)(x-4)
- How do you factorise 2x^2 - 4x - 6? 2(x+1)(x-3)
What Examiners Usually Test
- Ability to identify and factor out the greatest common factor.
- Correct application of the quadratic factorisation method.
- Understanding and applying the difference of two squares.