15 questions
9th - 12th Grade
Mathematics
This Grade 9–12 mathematics worksheet gives students focused practice with polynomial division, especially synthetic division. Across 15 multiple-choice questions, students organize polynomial coefficients, insert zero placeholders for missing terms, select the correct synthetic-division value from a linear factor, identify quotients and remainders, and write division results in proper form. Several items also ask students to evaluate or identify a remainder when a polynomial is divided by a factor such as x − 5, x − 3, or x + 1. The questions are designed to strengthen accuracy with signs, coefficient order, quotient degree, and remainder notation while giving teachers opportunities to identify procedural errors. Students in Algebra or other secondary mathematics courses can use the worksheet for guided practice, independent review, or a quick check of polynomial-division fluency. It is a free printable worksheet with a complete answer key, making it practical for classroom instruction, homework, or assessment preparation.
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WorksheetsAnswer KeyCam did not use a zero place holder for the x3 term.
2x3-x2-25x-12
71
3
C
This worksheet covers polynomial division through 15 multiple-choice questions focused largely on synthetic division. Students practice ordering coefficients, using zero placeholders for missing powers, choosing the correct divisor value, finding quotients and remainders, and writing answers in proper quotient-and-remainder form.
Introduce the coefficient-ordering items first, emphasizing that a missing term such as x³ must be represented by a zero coefficient. Then model how the factor determines the synthetic value—for example, x − 2 uses 2, while x + 3 uses −3—and have students apply the process to the quotient and remainder questions. Use the error-analysis item about a missing zero placeholder as a discussion prompt before assigning the remaining multiple-choice problems independently.
Watch for students omitting a zero placeholder when a polynomial lacks a power, using the wrong sign for the synthetic value, or confusing the final synthetic-division entry with a quotient coefficient. Students may also write the quotient with the original polynomial’s degree or misstate the remainder, so check that the quotient degree is one less than the dividend’s degree and that the remainder is reported separately when required.
The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for the 15 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app. The printable format also supports classrooms that are reducing screen time.
Under the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the coefficient arrays, polynomial expressions, and answer choices easier to scan. You can also enable a dyslexia-friendly font or translate the worksheet into another language while retaining the synthetic-division question format.
Wayground offers a broad collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
