Factoring Out the Greatest Common Factor
I can factor out the greatest common factor of a polynomial and check it by multiplying back.
What students learn
Students learn to find the GCF of a polynomial's terms, write the polynomial as the GCF times a parenthesized factor, and verify that it multiplies back and that nothing common is left.
See inside
The key rule
Divide every term by the GCF; a term equal to the GCF leaves 1, not a blank. Multiply back to check.
ab + ac = a(b + c)
Then read the ( ): if its terms share a factor other than one, the GCF was not the greatest.
Watch out
For 7x² + 7x, a student writes 7x(x).
The mistake: 7x² ÷ (7x) = x; then nothing, so 7x(x)7x(x) multiplies back to only 7x².
The fix: 7x ÷ (7x) = 1, so 7x(x + 1)A term equal to the GCF leaves 1.
The mistakes it targets
- Leaves a blank where a 1 belongs
- Divides the exponents instead of subtracting them
- Keeps the signs when dividing by a negative GCF
- Takes out a common factor that is not the greatest
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
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.