x² + 7x + 12
Show answer
(x + 3)(x + 4)
Free printable worksheet
Factoring Trinomials Worksheet
Twenty monic trinomials with positive and negative factor pairs.
Algebra 1Grades 7-103 pagesAnswer key included
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What this worksheet includes
- Twenty monic trinomials with positive and negative factor pairs.
- 3-page printable PDF with a complete answer key
- Designed for Grades 7-10 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this factoring trinomials worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 7-10 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach factoring trinomials
Factoring a monic trinomial reverses polynomial multiplication. For x² + bx + c, look for two integers whose product is c and whose sum is b.
The signs of b and c narrow the choices: a positive constant gives matching signs, while a negative constant gives opposite signs. Multiplying the factors is the fastest way to check the result.
Learning objectives
- Find factor pairs efficiently
- Use coefficient signs to choose factors
- Verify factors by multiplication
Skills to review first
- Integer factor pairs
- Combining like terms
- Multiplying binomials
Worked example
Follow the reasoning step by step
Factor x² + 5x + 6.
- List factor pairs of 6: 1 and 6; 2 and 3.
- Choose 2 and 3 because 2 + 3 = 5.
- Write (x + 2)(x + 3).
- Check by multiplying to recover x² + 5x + 6.
Solution: (x + 2)(x + 3).
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
x² − x − 12
Show answer
(x − 4)(x + 3)
x² − 9x + 20
Show answer
(x − 4)(x − 5)
Error check
Common mistakes to watch for
- Using factors that multiply correctly but add incorrectly
- Losing the sign of the middle term
- Stopping before checking for a greatest common factor