How to factorise on IGCSE 0580

Factorisation is one of the highest-frequency algebra skills on Cambridge IGCSE 0580. It shows up directly as "Factorise completely…" and indirectly as a step inside larger algebra and quadratic-equation problems.

Four patterns you must recognise on sight

• Common factor: 6x + 9 = 3(2x + 3). Always check first.
• Difference of two squares: a² − b² = (a − b)(a + b).
• Quadratic trinomial: x² + bx + c = (x + p)(x + q) where p + q = b and p × q = c.
• Grouping (4 terms): pair up, factor each pair, then take out the common bracket.

Common mark losses

• Stopping at "incomplete" factorising — the question says "completely". Check every bracket.
• Sign errors when factorising with a leading minus.
• Missing the difference of two squares because the squares aren't obvious (4x² − 25 = (2x − 5)(2x + 5)).