Free Printable WorksheetMathPre-CalculusMath CurriculumPre-CAL.33

Pre CAL.33 Polynomial Division and the Remainder Theorem Worksheet

Download our free printable Pre-Calculus Math worksheet on Pre CAL.33 Polynomial Division and the Remainder Theorem. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Polynomial Division and the Remainder Theorem Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.33 Polynomial Division and the Remainder Theorem. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.33 Polynomial Division and the Remainder Theorem - Polynomial Division and the Remainder Theorem

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.33 Polynomial Division and the Remainder Theorem skill assessments:

Problem 1Difficulty: Mastery

Let p(x) = 9x⁶ + 2x⁵ + 9x⁴ − 7x³ − x² − 3x + 6. Find the remainder r(x) when dividing by (x² − 2x − 15).

A18073x + 61221

B18074x + 61219

C18074x + 61223

D18074x + 61221

Solution & Explanation:The remainder must be linear, r(x)=ax+b. Divide p(x) by (x² − 2x − 15) (or use r(u)=p(u), r(v)=p(v)) to get r(x) = 18074x + 61221.

Problem 2Difficulty: Mastery

Let p(x) = x⁶ − 2x⁵ − 3x⁴ + x³ − 6x² + 7x − 6. Find the remainder r(x) when dividing by (x² − 1).

A6x − 14

B6x − 17

C5x − 14

D8x − 14

Solution & Explanation:The remainder must be linear, r(x)=ax+b. Divide p(x) by (x² − 1) (or use r(u)=p(u), r(v)=p(v)) to get r(x) = 6x − 14.

Problem 3Difficulty: Mastery

Let p(x) = 10x⁶ − x⁵ + 2x⁴ + 9x³ + 8x² − 10x + 6. Find the remainder r(x) when dividing by (x² − 6x + 5).

A38908x − 38884

B38910x − 38884

C38908x − 38883

D38906x − 38884

Solution & Explanation:The remainder must be linear, r(x)=ax+b. Divide p(x) by (x² − 6x + 5) (or use r(u)=p(u), r(v)=p(v)) to get r(x) = 38908x − 38884.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this Pre CAL.33 Polynomial Division and the Remainder Theorem worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this Pre CAL.33 Polynomial Division and the Remainder Theorem worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice Pre CAL.33 Polynomial Division and the Remainder Theorem online with instant feedback?

Yes! In addition to this printable worksheet, students can practice Pre CAL.33 Polynomial Division and the Remainder Theorem interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard Pre-CAL.33 (Polynomial Division and the Remainder Theorem).