Factoring by Grouping
I can factor a four-term polynomial by grouping, using the matching binomial as a check.
What students learn
Students learn to split four terms into two pairs, take the GCF out of each (a negative one when the second pair starts with a minus), factor out the matching binomial, and test whether a factor factors again.
See inside
The key rule
Both pairs must leave the same binomial. If they differ, recheck each GCF or reorder the terms.
a(x + k) + b(x + k) = (x + k)(a + b)
Every polynomial on this sheet starts with a positive term.
Watch out
A student factors 2x³ + 6x² − 5x − 15 and writes 2x²(x + 3) − 5(x − 3).
The mistake: −5x − 15 = −5(x − 3)−5(x − 3) is −5x + 15, and the binomials differ.
The fix: −5x − 15 = −5(x + 3), so (x + 3)(2x² − 5)With −5 out, both pairs leave x + 3.
The mistakes it targets
- Gets the sign wrong in the GCF or inside the parentheses
- Gives up when the pairs in the given order share nothing
- Stops before every factor is finished
- Leaves the grouped sum as the answer
The interactive Teacher Deck (31 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 (three 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.