Printable Synthetic Division Worksheet | Grade 11 Algebra II

This worksheet teaches Grade 11 Algebra II students to decide when synthetic division applies and then use it accurately. Students divide polynomials by linear divisors, interpret quotients and remainders, use the Remainder Theorem, and rebuild polynomials from division results, finishing with factoring and zero-finding challenges.

At a Glance

• Grade: 11 · Subject: Algebra II
• Standard: HSA-APR.D.6 — Divide polynomials by x − c with synthetic division and use remainders
• Skill Focus: Synthetic division with valid linear divisors
• Format: 5 pages · 18 problems · Answer key included · PDF
• Best For: Polynomial division practice after direct instruction
• Time: 35–45 minutes

What's Inside

Students complete 18 tasks in a 5-page PDF: a multiple-choice check on valid divisors, guided setups, divisions with quotient-and-remainder answers, table completion, error analysis, and zero-finding. A rule reminder box states when synthetic division is valid and lists the answer conventions. The answer key shows quotients, remainders, and key steps.

Skill Progression

• Guided practice: 4 Part A problems with the rule box and setup prompts for coefficient rows and the value of c.
• Supported practice: 10 Part B problems on remainder form, factoring, rebuilding P(x), completing a table, finding k, fractional c, and error analysis.
• Independent practice: 4 Part C challenges on rewriting 2x − 1, repeated zeros, successive divisions, and remainders by a quadratic.

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

Standards Alignment

HSA-APR.D.6 — Rewrite a(x)/b(x) in the form q(x) + r(x)/b(x) using inspection, long division, or, for complicated examples, a computer algebra system. This worksheet targets the linear-divisor case. The standard code can be copied directly into lesson plans, IEP goals, or district curriculum mapping tools.

How to Use It

• During instruction: Assign Parts A and B as guided classwork right after teaching the method.
• After instruction: Send the sheet home or use it as unit-test review, with Part C as extension.

Formative tip: while students work, check that they write 0 for missing powers and use the correct sign for c, the two most common setup errors. Expect 35–45 minutes for the full sheet.

Who It's For

Grade 11 Algebra II students learning polynomial division. Assign Parts A and B to students who need support and add Part C for advanced learners. Pair it with a worked-example anchor chart on synthetic division or a Remainder Theorem lesson.

HSA-APR.D.6 asks students to rewrite a rational expression a(x)/b(x) as q(x) + r(x)/b(x), and synthetic division is the fastest hand method when the divisor has the form x − c. This Grade 11 Algebra II worksheet gives students 18 problems that teach them to check whether a divisor is valid, set up coefficient rows with zeros for missing powers, and read the quotient and remainder correctly. Tasks also connect division to the Remainder Theorem, factor testing, polynomial reconstruction, and error analysis. Fisher & Frey (2014) describe gradual release of responsibility as a way to move learners from guided to independent work, and this worksheet follows that sequence across three parts. Teachers can use it as classroom practice, homework, or a quick formative check on procedural fluency and conceptual understanding of polynomial division in about 40 minutes.