(2x² + 3x) + (x² − 5x + 4)
Show answer
3x² − 2x + 4
Free printable worksheet
Polynomial Operations Worksheet
Fourteen problems covering addition, subtraction, distribution, and multiplication.
Algebra 1Grades 7-104 pagesAnswer key included
No email is required. Download the complete worksheet and answer key now.
Download the free PDF
What this worksheet includes
- Fourteen problems covering addition, subtraction, distribution, and multiplication.
- 4-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 polynomial operations 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 polynomial operations
Polynomial operations depend on recognizing like terms. Addition and subtraction combine terms with matching variable parts, while multiplication distributes every term in one factor across every term in the other.
When subtracting a polynomial, distribute the negative sign before combining terms. Final answers should be arranged in descending order of degree with no like terms remaining.
Learning objectives
- Add and subtract polynomials
- Distribute monomials and multiply binomials
- Write results in standard form
Skills to review first
- Combining like terms
- The distributive property
- Exponent product rules
Worked example
Follow the reasoning step by step
Subtract (x² + 4x − 1) from (3x² − 2x + 5).
- Write (3x² − 2x + 5) − (x² + 4x − 1).
- Distribute the subtraction: 3x² − 2x + 5 − x² − 4x + 1.
- Combine quadratic, linear, and constant terms.
- Arrange the result in descending degree.
Solution: 2x² − 6x + 6.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
3x(2x² − x + 5)
Show answer
6x³ − 3x² + 15x
(x + 3)(x − 2)
Show answer
x² + x − 6
Error check
Common mistakes to watch for
- Combining terms with different exponents
- Distributing a negative sign to only the first term
- Failing to multiply every pair of terms