Printable Polynomial Long Division Worksheet | Algebra 9

Master the mechanics of algebraic division with this comprehensive practice set. This resource focuses on polynomial long division, enabling students to find quotients and remainders for quadratic and linear expressions. By working through these problems, learners solidify their understanding of the division algorithm, preparing them for complex rational functions and higher-level calculus concepts.

At a Glance

• Grade: 9 · Subject: Algebra
• Standard: HSA-APR.D.6 — Rewrite rational expressions into quotient and remainder forms
• Skill Focus: Polynomial Long Division
• Format: 5 pages · 10 problems · Answer key included · PDF
• Best For: High school algebra independent practice sessions
• Time: 30–45 minutes

This five-page PDF collection contains ten carefully selected polynomial division problems. Each page features two large workspace areas, allowing students to show their step-by-step long division work clearly. The set includes a full answer key, ensuring that teachers and students can verify quotients and remainders quickly. The layout is clean and distraction-free to maintain student focus on mathematical operations.

Skill Progression

• Guided practice: The initial problems involve monic divisors and quadratic dividends, establishing the core routine of divide, multiply, subtract, and bring down.
• Supported practice: Middle problems introduce missing terms and negative coefficients, requiring students to maintain careful alignment and sign tracking.
• Independent practice: Final challenges include non-monic divisors and complex remainders, testing mastery of the algorithm in diverse algebraic scenarios.

This progression follows the gradual-release model, moving from predictable structures to more demanding division tasks.

Standards Alignment

This resource aligns with CCSS.MATH.CONTENT.HSA.APR.D.6, which requires students to rewrite simple rational expressions in different forms. Specifically, it focuses on writing algebraic fractions in the form of a quotient plus a remainder over the divisor. This standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

Distribute this worksheet as a primary practice set during the independent phase of a direct instruction lesson on polynomial division. It also serves as an effective formative assessment tool; teachers can observe students working on problems 3 and 4 to identify common errors in subtraction or term alignment. Expect students to complete the full 10-problem set within 35 minutes.

Who It's For

This set is designed for Grade 9 Algebra students or Grade 8 advanced learners who are tackling rational expressions. It is particularly useful for students who benefit from ample workspace to prevent computational errors. Pair this resource with a step-by-step anchor chart or a video tutorial on the long division algorithm.

The polynomial long division algorithm remains a cornerstone of high school algebra, serving as the bridge between basic arithmetic and the manipulation of complex rational functions. According to a ScienceDirect TpT Analysis, structured drill practice in algebraic algorithms is essential for developing the procedural fluency required for success in Calculus. This worksheet addresses HSA-APR.D.6 by requiring students to rewrite rational expressions into their quotient and remainder components, a task that demands precision in term alignment and sign management. Research by Fisher & Frey (2014) highlights that the gradual release of responsibility, supported by ample workspace for modeling mathematical thinking, significantly improves student retention of algorithmic steps. By completing these 10 tasks, students move beyond simple memorization to a functional understanding of how polynomial structures interact during division, providing a stable foundation for identifying horizontal and slant asymptotes in future units.