Factoring Trinomials with Leading Coefficient 1
I can factor a trinomial of the form x squared plus bx plus c by finding the pair that multiplies and adds.
The problem this sheet solves
Students find a genuine factor pair and put the signs the wrong way round. Both (x minus 5)(x plus 3) and (x plus 5)(x minus 3) give minus 15, so the check students reach for first is exactly the one that cannot see the error. The pair has to do TWO jobs, multiply to c and add to b, and students stop after the job they went looking for. The factor-pair table lists every pair of c WITH its sum, so the pair that does both jobs is picked rather than hunted. The area box explains why: the two middle cells of the 2x2 are the two numbers times x, and they ADD to the middle term. Every item is checkable by multiplying back, which is the habit the previous sheet installed.
The key rule
Find the pair that multiplies to the constant AND adds to the middle coefficient. Both jobs, or it is the wrong pair, whatever the constant looks like.
Multiply to c. Add to b.
Watch out
The mistake: For x2 + 2x − 15 a student writes (x − 5)(x + 3).
The fix: (x + 5)(x − 3). Their pair multiplies to −15, so the constant cannot tell the two apart. It adds to −2, not +2.
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.