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Long Division with Polynomials - Printable Mathematics Worksheets - Wayground

Long Division with Polynomials

20 questions

10th - 10th Grade

Mathematics

Long Division with Polynomials is a Grade 10 mathematics worksheet with 20 multiple-choice questions that develops fluency in dividing polynomial expressions. Students determine polynomial quotients, identify quotient-and-remainder forms, and evaluate whether a completed polynomial-division solution is correct. The examples require careful attention to coefficients, powers, signs, and remainders. The worksheet also includes practice with adding, multiplying, and simplifying radical expressions, including products such as √10 · √45. This mixed format gives teachers a focused way to check whether students can carry out algebraic procedures and recognize correct simplified results. Use it for independent practice, review, or a quick formative assessment. It is a free printable worksheet with an answer key for Grade 10 math instruction.

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Worksheets

Long Division with Polynomials

Total questions: 20

Name
Class
Date
1.

a)

A

b)

B

c)

C

d)

D

2.

a)

A

b)

B

c)

C

d)

D

3.

a)

A

b)

B

c)

C

d)

D

4.

a)

A

b)

B

c)

C

d)

D

5.

a)

A

b)

B

c)

C

d)

D

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

A

b)

B

c)

C

d)

D

8.
a)

2x - 4

b)

2x + 4

c)

2x - 1 + -16/4x-5

d)

2x - 4 + -40/4x-5

9.

(27x3 + 9x2 - 3x - 10) ÷ (3x - 2)

a)

9x4+5

b)

9x2+9x+5

c)

9x2-9x+5

d)

9x2-9x

10.

(3x3 + 5x - 1) ÷ (x + 1)

a)

3x3 - 3x2 + 8x - 9

b)

3x2 - 3x + 8 - 9/x+1

c)

3x2 + 3x + 8 + 7/x+1

d)

3x3 + 3x2 + 8x + 7

11.
a)
2x3 + 3x + (7/x-4)
b)
2x2 + 3x + 8 + (7/x-4)
c)
2x2 + 3x + 8
d)
2x2 - x + 10 + (6/x-4)
12.
a)

2x2 + 3x + 8 + -57/x-4

b)

2x2 - 13x - 56

c)

2x2 + 3x + 8 +7/x-4

d)

2x2 - 3x - 16 + -89/x-4

13.

a)

A

b)

B

c)

C

d)

D

14.

(x3-8x2+6x+41)÷(x-4)

a)

x2-4x-7, R 2

b)

x2-4x-11, R 1

c)

x2-2x-12, R 3

d)

x2-4x-10, R 1

15.
Is this division problem worked correctly?
a)
This is correct!
b)
This is incorrect!
16.

Add the radicals below

5+20\sqrt[]{5}+\sqrt[]{20}  

Hint: Simply 20\sqrt[]{20} first.

a)

5

b)

555\sqrt[]{5}  

c)

353\sqrt[]{5}  

d)

10

17.

Multiply the radical expressions and simplify the result.

5⋅10\sqrt[]{5}\cdot\sqrt[]{10}  

a)

50\sqrt[]{50}  

b)

252\sqrt[]{5}  

c)

525\sqrt[]{2}  

d)

50

18.

Multiply and simplify:

6⋅6\sqrt[]{6}\cdot\sqrt[]{6}  

a)

36\sqrt[]{36}  

b)

232\sqrt[]{3}  

c)

  6\sqrt[]{6}  

d)

6

19.

Multiply and simplify

3⋅15\sqrt[]{3}\cdot\sqrt[]{15}  

a)

353\sqrt[]{5}  

b)

535\sqrt[]{3}  

c)

  959\sqrt[]{5}  

d)

45\sqrt[]{45}  

20.
Simplify:
√10 ⋅ √45
a)
3√50
b)
8√2
c)
√450
d)
15√2
Answer Key

Long Division with Polynomials

Total questions: 20

1.
b)

B

2.
b)

B

3.
d)

D

4.
b)

B

5.
b)

B

6.
a)

A

7.
a)

A

8.
b)

2x + 4

9.
b)

9x2+9x+5

10.
b)

3x2 - 3x + 8 - 9/x+1

11.
b) 2x2 + 3x + 8 + (7/x-4)
12.
c)

2x2 + 3x + 8 +7/x-4

13.
d)

D

14.
d)

x2-4x-10, R 1

15.
b) This is incorrect!
16.
c)

353\sqrt[]{5}  

17.
c)

525\sqrt[]{2}  

18.
d)

6

19.
a)

353\sqrt[]{5}  

20.
d) 15√2

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FAQs

What does this Long Division with Polynomials worksheet cover?

This Grade 10 mathematics worksheet uses 20 multiple-choice questions to practice dividing polynomials, finding quotients and remainders, and checking whether a worked division solution is correct. It also includes items on adding, multiplying, and simplifying radical expressions, so students must apply algebraic procedures and select the correctly simplified result.

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

Model one division problem by organizing the dividend in descending powers, dividing the leading terms, multiplying back, and subtracting before repeating the process. Then have students use the multiple-choice items to explain why a quotient or quotient-with-remainder option is correct, and use the question about an incorrectly worked solution to discuss where a sign, coefficient, or subtraction step went wrong. Finish with the radical items as a short comparison of polynomial and radical simplification procedures.

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

Watch for students losing negative signs while subtracting, omitting a power when a polynomial term is missing, or reporting the quotient without the remainder. In the radical questions, students may multiply coefficients and radicands incorrectly, combine unlike radicals, or stop before reducing the result to simplest form, as required by items such as √10 · √45.

How do I assign and grade this polynomial division worksheet?

On Wayground, assign Long Division with Polynomials either as a printable PDF or as a digital quiz. The worksheet includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also provides an option for schools seeking to reduce screen time.

Does this worksheet include practice beyond polynomial division?

Yes. Alongside multiple-choice polynomial-division problems and a question asking students to judge a worked solution, the worksheet includes questions on adding radicals, multiplying radical expressions, and simplifying products such as √10 · √45. These items let you check students’ ability to simplify both polynomial and radical expressions within one Grade 10 review.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive 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.

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