Factorising
Single bracket, quadratic (double bracket), and difference of two squares (DOTS). Both tiers.
Three core types: single bracket (common factor), quadratic factorising (find two numbers that sum to b and multiply to ac), DOTS (a² - b² = (a+b)(a-b)).
Worked examples
x² + 5x + 6 = (x+2)(x+3). 2×3=6, 2+3=5.
x² − 9 = (x+3)(x−3). DOTS.
2x² + 7x + 3 = (2x+1)(x+3). Higher: harder quadratics (a ≠ 1).
Frequently asked questions
How do I factorise 2x² + 7x + 3?
Multiply outer constants: 2×3=6. Find two numbers summing to 7 multiplying to 6: 6 and 1. Split: 2x²+6x+x+3 → 2x(x+3)+1(x+3) = (2x+1)(x+3).
How do I spot DOTS?
Two squared terms separated by a minus. x² − 16, 4x² − 25, x² − y². Each factorises as (a+b)(a−b).