Lesson 3 of 4 · about 30 minutes · Win: look at an expression and name the right rule from your notes before you start writing.
You already know the five rules from term1.pdf pp.1–4 and the cubic method from pp.23–24. The hard part is recognising which one fits. The trick is to stop asking “how do I factorise this?” and ask a fixed list of questions in order, mostly about how many terms there are and what kind they are.
Print this now and keep it next to you: Factoring decision guide (flowchart).
For each expression, choose the rule you would use first. Then read the clue and the full factorisation, and check it against what you would have written. The problems are mixed on purpose: that’s what the test will feel like. (Every button list is in the same order, so its position gives nothing away.)
Problems are from term1.pdf (page shown) or modelled on them. Have paper ready: after you pick the rule, factorise it yourself before you read the solution.
Primary: term1.pdf pp.1–4 (rules 1–5) and pp.23–28 (cubics, factor theorem, synthetic division). External: Paul’s Online Notes – Factoring Polynomials (same order: common factor, grouping, trinomials, special forms) and Dividing Polynomials for synthetic division.
Real exam questions on this: lesson 5, past exam questions.