Free Polynomial Division Worksheet | Grade 11 Algebra II

This Grade 11 Algebra II worksheet helps students connect polynomial degree to the structure of division. Students use the identity a(x) = b(x)·q(x) + r(x) to predict quotient and remainder degrees, divide with long and synthetic division, and rewrite results as q(x) + r(x)/b(x).

At a Glance

• Grade: 11 · Subject: Algebra II
• Standard: HSA-APR.D.6 — Rewrite a rational expression as a quotient plus remainder over the divisor
• Skill Focus: Polynomial degree and division structure
• Format: 5 pages · 16 problems · Answer key included · PDF
• Best For: Unit practice after division instruction
• Time: 45–60 minutes

What's Inside

The worksheet opens with a rules box covering degree rules, the division identity, setup for missing powers, and the remainder fact. Three parts follow: four multiple-choice concept questions, eight short applications (including a degree table), and four explanation and transfer tasks. A 3-page answer key is included.

Skill Progression

• Guided practice: 4 concept-distinction questions with answer choices that expose common degree and remainder misconceptions.
• Supported practice: 8 applications covering long division, synthetic division, division by 3x − 1, and reconstructing a dividend, with the rules box as a scaffold.
• Independent practice: 4 tasks that ask students to find an error, model a box volume, justify a degree rule, and solve a remainder problem.

The sequence follows gradual release: I Do, We Do, You Do.

Standards Alignment

HSA-APR.D.6: Rewrite simple rational expressions in different forms, writing a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x). This standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

Assign Parts A and B after direct instruction on long and synthetic division, then use Part C as a closing review. While students work, watch whether they insert zero coefficients for missing powers; that is the most telling formative check. Expect 45–60 minutes.

Who It's For

Algebra II students in the polynomial operations unit, including those preparing for precalculus. Students who need support can work Part A first with the rules box open. It pairs well with an anchor chart on synthetic division setup.

HSA-APR.D.6 asks students to rewrite a(x)/b(x) as q(x) + r(x)/b(x) using inspection or long division. This Grade 11 Algebra II worksheet builds that skill through 16 tasks across 5 pages, linking polynomial degree rules to the division identity, synthetic division, the remainder fact, and applied contexts such as box volume. Students predict quotient and remainder degrees before computing, then explain errors in worked solutions. Explicit scaffolds like a rules box and placeholder-term reminders reflect guided instruction principles described by Fisher & Frey (2014), who show that gradual release of responsibility moves learners from teacher modeling to independent application. A 3-page answer key supports quick feedback. Every answer is exact and written in standard form, so students practice precise notation alongside procedure. The set suits unit practice, review, and formative checks in Algebra II courses that cover polynomial operations and division.