Term 1 Week 7 · Factoring polynomials completely · CG Quarter 1, competency 8
| # | The misconception | Where it shows | What to do |
|---|---|---|---|
| 1 | Only one factorisation can be correct | §B, by design | Expand all three. The arithmetic settles it, not the teacher |
| 2 | Incomplete means wrong | Exit ticket item 1 | Correct immediately. Factoring proceeds in stages and every stage is correct |
| 3 | A common factor of 2 "does not count" | Answer B left as final | 2x − 4 = 2(x − 2). A numerical common factor is still a factor |
| 4 | Complete means "as many brackets as possible" | Learner writes 2(x−2)(x+2) as (2)(x−2)(x+2) and asks if it is more complete | Both are the same. The 2 is a factor whether or not it has brackets round it |
| 5 | x² + 4 factors like x² − 4 | Will appear on Day 3, but sometimes today | Defer it explicitly: "Hold that question until Wednesday — it is a good one." Write the learner's name on the board beside it |
| 6 | Factoring is guessing | Learners wait to be told | Every answer is checkable by expanding. Nobody needs permission to know if they are right |
| 7 | The common factor must be a number | 5x² + 15x → 5(x² + 3x), stopping there | The bracket still has an x in every term. Push: "Look again." |