M4.9.2 For the adult
Factorising quadratics
I can expand (x + 3)(x + 4) to get x² + 7x + 12. How do I go backwards?
What this chapter teaches
Factorising undoes expanding. For x² + bx + c, find two numbers that multiply to c and add to b. A difference of two squares, like x² − 49, factorises into (x + 7)(x − 7). Always check by expanding.
Three questions to ask
There is no one right wording. Listen for the idea.
- Which two numbers multiply to 12 and add to 7, and how do you know?
- Why does x² − 49 factorise with one plus and one minus?
- How can you check a factorisation without trusting your arithmetic twice?
After the chapter, the learner can
- Factorise x² + 7x + 12
- Factorise a difference of two squares, like x² − 49
- Factorise 2x² + 7x + 3
What they copy into their notebook
Find two numbers that multiply to the last number and add to the x number. Check the signs. Look for a common factor first. Expand to check.