M4.9.3 For the adult
Using factorising
I factorised x² − 5x + 6 = 0 into (x − 2)(x − 3) = 0. What does that say about x?
What this chapter teaches
If two numbers multiply to give 0, one of them is 0. So a quadratic with 0 on one side and brackets on the other has its solutions found bracket by bracket. Dividing by x loses a solution, and only a whole bracket can cancel in a fraction.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why does (x − 2)(x − 3) = 0 give x = 2 or x = 3?
- What goes wrong if you divide both sides of x² = 5x by x?
- Why can you cancel (x + 3) in (x² − 9)/(x + 3), but not the 3 in (x + 3)/3?
After the chapter, the learner can
- Solve x² − 5x + 6 = 0 by factorising
- Explain why ab = 0 means a = 0 or b = 0
- Simplify (x² − 9)/(x + 3) by factorising
What they copy into their notebook
Make one side 0. Factorise. A product is 0 only if a factor is 0, so put each bracket equal to 0. Do not divide both sides by x: x may be 0. Cancel only whole brackets.