Factoring Trinomials with a Leading Coefficient
I can factor ax² + bx + c by finding the pair that multiplies to a · c and adds to b.
What students learn
Students learn to factor a trinomial ax² + bx + c: they take out any GCF, find the pair with product a · c and sum b, split the middle term, read the factors off the box and verify by multiplying back.
See inside
The key rule
Multiply a · c, find the pair that adds to b, split the middle term, then read the box's edges.
p · q = a · c and p + q = b
When a = 1, a · c is just c: the same two jobs as before.
Watch out
A student says 3x² + 7x + 2 does not factor: no pair of 2 adds to 7.
The mistake: pairs of 2: 1 + 2 = 3, never 7The pair multiplies to a · c, not to c.
The fix: 3 · 2 = 6; 1 + 6 = 7, so (3x + 1)(x + 2)It factors: the pair is 1 and 6.
The mistakes it targets
- Looks for the pair from c alone and says it does not factor
- Swaps the constants between the two factors
- Gets the signs in the factors wrong
- Leaves out or skips the GCF
The interactive Teacher Deck (33 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 (five 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.