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Long Division Polynomials - Printable Mathematics Worksheets - Wayground

Long Division Polynomials

16 questions

9th - 12th Grade

Mathematics

Long Division Polynomials is a free printable mathematics worksheet for students in Grades 9–12. It develops polynomial long-division skills through 16 items: five fill-in-the-blank questions that require students to identify missing terms or calculate remainders, and 11 multiple-choice questions that ask them to evaluate worked solutions, identify the first line containing an error, select a correct division method, and determine whether a binomial is a factor. The worksheet also prompts students to check explanations and reflect on whether they understand their mistakes. These self-check items reinforce careful review of polynomial division steps, signs, quotient structure, and remainder results rather than answer selection alone. It is suitable for guided practice, independent work, or review before assessment, and includes a complete answer key for efficient checking.

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Long Division Polynomials

Total questions: 16

Name
Class
Date
1.

Identify the missing term to complete the solution.

(a)  

2.

Use the image to check your work for the previous question.

a)

I checked my work and I understand my mistake

b)

I checked my work and I do not understand my mistake

c)

I got the last question correct

d)

I did not check my work

3.

Identify the missing term to complete the solution.

(a)  

4.

Use the image for the explanation for the previous question.

a)

I checked the explanation and I understand my mistake

b)

I checked the explanation and I do not understand my mistake

c)

I got the last question correct

5.

Is this division problem worked correctly? If there is an error, on which line does the FIRST error occur?

a)

This is correct!

b)

This is incorrect, and error occurs on the 2nd line!

c)

This is incorrect, and the error occurs on the 4th line!

d)

This is incorrect, and the error occurs on the 3rd line!

6.

Use the image for the explanation for the previous question.

a)

I checked the explanation and I understand my mistake

b)

I checked the explanation and I do not understand my mistake

c)

I got the last question correct

7.

Which of the following is the correct way to solve when a3 - 4 is divided by a+2?

a)

b)

-6

8.

Use the image for the explanation for the previous question.

a)

I checked the explanation and I understand my mistake

b)

I checked the explanation and I do not understand my mistake

c)

I got the last question correct

9.

What is the remainder for 4x3−2x2+6x−82x\frac{4x^3-2x^2+6x-8}{2x} ?

(a)  

10.

Use the image to check your work for the previous question.

a)

I checked my work and I understand my mistake

b)

I checked my work and I do not understand my mistake

c)

I got the last question correct

d)

I did not check my work

11.

What is the remainder when (48y2 + 8y + 7) ÷ (12y - 1)?

(a)  

12.

Use the image to check your work for the previous question.

a)

I checked my work and I understand my mistake

b)

I checked my work and I do not understand my mistake

c)

I got the last question correct

d)

I did not check my work

13.
            Is (x-2) a factor of             f(x)= x3-8x2+14x-4?
a)
Yes, (x-2) is a factor. There is a remainder.
b)
No, (x-2) is  not a factor. The remainder is zero.
c)
Yes, (x-2) is a factor. The remainder is zero.
d)
No, (x-2) is  not a factor. There is a remainder. 
14.

Use the image to check your work for the previous question.

a)

I checked my work and I understand my mistake

b)

I checked my work and I do not understand my mistake

c)

I got the last question correct

d)

I did not check my work

15.

What is the remainder for 3x4+4x3−5x2+14x−17x2+2x−2\frac{3x^4+4x^3-5x^2+14x-17}{x^2+2x-2} ?

(a)  

16.

Use the image for the explanation for the previous question.

a)

I checked the explanation and I understand my mistake

b)

I checked the explanation and I do not understand my mistake

c)

I got the last question correct

Answer Key

Long Division Polynomials

Total questions: 16

1.
7, 7, 7
2.
n/a
3.
-5, - 5, -5, - 5
4.
n/a
5.
b)

This is incorrect, and error occurs on the 2nd line!

6.
n/a
7.
b)

8.
n/a
9.
-4, - 4, -4, - 4
10.
n/a
11.
8, 8, 8
12.
n/a
13.
c) Yes, (x-2) is a factor. The remainder is zero.
14.
n/a
15.
-7, - 7, -7, - 7
16.
n/a

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FAQs

What does the Long Division Polynomials worksheet cover?

This worksheet covers polynomial long division through missing-term fill-in-the-blank problems, remainder calculations, multiple-choice analysis of worked solutions, and a factor check using a polynomial and binomial. Students build accuracy by completing division steps, locating the first error in an incorrect solution, interpreting remainders, and connecting a zero remainder with a factor conclusion.

How can I use this worksheet to teach polynomial long division?

Introduce the worksheet by modeling one polynomial division problem and emphasizing the sequence of divide, multiply, subtract, and bring down. Then have students complete the missing-term and remainder items before using the multiple-choice error-analysis questions to discuss why an incorrect line changes the rest of the solution. Ask students to use each explanation prompt to identify whether their mistake came from a sign, a multiplication step, subtraction, or interpretation of the remainder.

What mistakes should I watch for when students complete this polynomial division worksheet?

Watch for skipped or misordered division steps, sign errors when subtracting polynomial terms, and incorrect missing terms in the quotient. Students may also identify a later line instead of the first line containing an error, or confuse a nonzero remainder with a factor relationship. The worksheet’s self-check questions can reveal whether students corrected the work and understood the explanation rather than simply changing an answer.

How do I assign and grade the Long Division Polynomials worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for checking the five fill-in-the-blank and 11 multiple-choice items. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The PDF option can also support schools that are reducing screen time while preserving structured polynomial-division practice.

How can I differentiate this polynomial long division worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the polynomial expressions and multi-step division work have more visual room. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support access to the fill-in-the-blank, error-analysis, and remainder questions.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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