Choosing a Factoring Strategy
I can choose a factoring method by taking out the GCF and counting the terms that are left.
The problem this sheet solves
A mixed exercise set does not test any single method — it tests CHOOSING, which no single-method sheet ever asks for. Students reach for the pattern they recognise and apply it before the common factor comes out, and multiplying back confirms an answer that still has more in it. This sheet is a decision procedure rather than a seventh method. GCF first, always; then count the terms — two means a difference of squares, three means check for a perfect square before an ordinary trinomial, four means grouping. Nothing new is taught, and one item deliberately has no common factor at all, so a student who has learned always divide by something gets caught by the sheet rather than by a test.
The key rule
Take out the GCF, then count the terms left: two means difference of squares, three means a trinomial, four means grouping.
GCF. Then count.
Watch out
The mistake: For 4x2 − 100 a student writes (2x + 10)(2x − 10).
The fix: That multiplies back correctly and is still not finished — both brackets share a 2. Taking the GCF out first makes it impossible: 4(x2 − 25) = 4(x + 5)(x − 5).
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.