Factoring Trinomials with Leading Coefficient 1
I can factor x² + bx + c by finding the pair that multiplies to c and adds to b.
What students learn
Students learn to factor a trinomial x² + bx + c into (x + p)(x + q) by finding the pair with product c and sum b, using the signs of b and c, and verify it by multiplying back.
See inside
The key rule
List the pairs that multiply to c. Use the one that adds to b, then check by multiplying back.
x² + bx + c = (x + p)(x + q)
Here p · q = c and p + q = b: the pair has two jobs.
Watch out
For x² + 2x − 15, a student writes (x − 5)(x + 3).
The mistake: −5 · 3 = −15, so (x − 5)(x + 3)It multiplies back to x² − 2x − 15.
The fix: 5 + (−3) = 2, so (x + 5)(x − 3)The pair must add to +2, not −2.
The mistakes it targets
- Swaps the signs, so the product is right but the sum is wrong
- Makes both numbers positive when b is negative
- Stops at a pair that multiplies to c but does not add to b
- Writes a factor's sign apart from its number
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.