Aligned Polynomial Division Worksheet | Grade 11 Algebra II

This worksheet helps Grade 11 Algebra II students divide polynomials and prove their answers with the division identity a(x) = b(x)·q(x) + r(x). Across 16 problems, students find quotients and remainders, rebuild dividends, and rewrite results as q(x) + r(x)/b(x), moving from linear divisors to quadratic ones.

At a Glance

• Grade: 11 · Subject: Algebra II
• Standard: HSA-APR.D.6 — Divide polynomials and verify each result with the division identity.
• Skill Focus: Polynomial-division check
• Format: 5 pages · 16 problems · Answer key included · PDF
• Best For: Algebra II division practice and review
• Time: 40–50 minutes

What's Inside

The worksheet opens with a Conventions and Scoring box that states the division identity, reminds students to write missing powers with a coefficient of 0, and requires exact answers in descending order. Task types include long division, reconstructing a dividend from a quotient and remainder, multiple choice on the check equation, a degree-reasoning table, error analysis of a student claim, remainder-theorem problems, and solving for unknown coefficients. The 5-page packet comes with a 3-page answer key and a 32-point scoring scheme.

Skill Progression

• Guided practice: Part A has 4 Foundation problems (1 point each). A hint line points students to long division, the check identity, or degree reasoning.
• Supported practice: Part B has 8 Core problems (2 points each). Students show each division step or reconstruction, including a missing x³ term and a quadratic divisor.
• Independent practice: Part C has 4 Challenge problems (3 points each). Students find unknown coefficients, explain why two values determine a remainder, and state excluded x-values.

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

Standards Alignment

HSA-APR.D.6: Rewrite simple rational expressions in different forms. Write 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 and the degree of r(x) is less than the degree of b(x), using inspection or long division. The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

• After direct instruction: Assign Parts A and B as classwork once students have seen long division and the remainder theorem. Allow 25–30 minutes.
• Review or quiz prep: Assign Part C alone, or the full packet, as homework before a unit assessment. The full packet takes 40–50 minutes.

Formative tip: while students work, watch whether they insert 0 coefficients for missing powers and whether they test their answer with the check identity before moving on.

Who It's For

This packet suits Grade 11 Algebra II students learning polynomial operations and division. Students who need more support can stay with Part A and the worked conventions box, while advanced students can focus on Part C. Pair it with a direct-instruction lesson on synthetic and long division or a remainder theorem anchor chart.

Standard HSA-APR.D.6 asks students to divide polynomials and rewrite a(x)/b(x) as q(x) + r(x)/b(x). This Grade 11 Algebra II worksheet builds that skill through 16 tasks that all return to one idea: a quotient and remainder are only correct if b(x)·q(x) + r(x) rebuilds a(x). Its structure of 4 Foundation, 8 Core, and 4 Challenge problems reflects the gradual release of responsibility described by Fisher & Frey (2014), in which teacher modeling gives way to guided and then independent practice. Students practice verifying their own work, which supports accuracy, error analysis, and algebraic reasoning. A 32-point scoring guide and a 3-page answer key make the packet quick to grade and easy to use for formative assessment.