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dividing polynomials by monomials - Printable Math Worksheets class 10 - Wayground

dividing polynomials by monomials

Delphi Aubry

Created by Delphi Aubry

21 questions

9th - 12th Grade

Math

Updated Sept 2026

This free printable worksheet helps students in Grades 9–12 simplify polynomial expressions divided by monomials. Across 21 questions, including 3 fill-in-the-blank items and 18 multiple-choice problems, students divide coefficients and subtract exponents for each variable in every term. Problems include monomials with one or more variables, multi-term polynomials, and expressions with positive and negative terms. Students also practise identifying the correct quotient, applying the division rule to expressions such as fractions and parentheses, and entering simplified answers with caret notation for exponents when required. The worksheet is useful for independent practice, guided review, homework, or a quick skills check in an algebra unit. It is available as a free printable worksheet with a complete answer key, making it easier to review calculation steps and identify errors in coefficient or exponent operations.

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dividing polynomials by monomials

Total questions: 21

Name
Class
Date
1.

Simplify the expression. In your answer, use the carrot symbol for exponents. Example: For x2x^2 , type x^2

4k5 + 10k4 − 8k32k3\frac{4k^5\ +\ 10k^4\ -\ 8k^3}{2k^3}  

(a)  

2.

 5x2−15y35\frac{5x^2-15y^3}{5}  

a)

 x2−3y3x^2-3y^3  

b)

 x2−15y3x^2-15y^3  

c)

 10x2−20y310x^2-20y^3  

d)

 5x2−3y35x^2-3y^3  

3.
Question Image
a)
-5x10
b)
4x4 + 18x6
c)
-6x4 + 16x2
d)
4x4 - 9x2
4.
Divide the polynomial by the monomial.
Divide the polynomial by the monomial.
a)
15x9 - 8x3
b)
3x6 - 8x3
c)
-5x12
d)
3x6 - 40x3
5.

 m2n+m6n3mn\frac{m^2n+m^6n^3}{mn}  

a)

 m3n2+m7n4m^3n^2+m^7n^4  

b)

 m2n+m5n2m^2n+m^5n^2  

c)

 m+m5n2m+m^5n^2  

d)

 m+m6n3m+m^6n^3  

6.
Divide the polynomial by the monomial.
Divide the polynomial by the monomial.
a)
2x8-8x2-28x
b)
2x8-2x2-7x
c)
8x7-8x-28x
d)
2x7 -2x -7
7.
Find the quotient.

Find the quotient.

a)

-3a + 6b

b)

3a - 6b

c)

6a2b - 6b

d)

3a - 12ab

8.

 (14d3−21d8)÷ 7d2\left(14d^3-21d^8\right)\div\ 7d^2  

a)

 7d−21d67d-21d^6  

b)

 7d1.5−14d47d^{1.5}-14d^4  

c)

 2d−3d62d-3d^6  

d)

 2d1.5−3d42d^{1.5}-3d^4  

9.

When I am a dividing by a monomial, I should _______ the coefficients and ________ the exponents for each term.

a)

add, subtract

b)

subtract , divide

c)

divide, divide

d)

divide, subtract

10.
Question Image
a)
5w 2 − 4w + 3
b)
12w 2 − 9w + 6
c)
12w 2 − 12w + 9
d)
5w 2 − 12w+ 9
11.

Simplify 10x8y52x2y5\frac{10x^8y^5}{2x^2y^5}  

a)

5x6y5x^6y  

b)

5x105x^{10}  

c)

5x45x^4  

d)

5x65x^6  

12.
Question Image
a)
5w 2 − 4w + 3
b)
12w 2 − 9w + 6
c)
12w 2 − 12w + 9
d)
5w 2 − 12w+ 9
13.

 6a3b2c4 − 8a2b2c2a2bc\frac{6a^3b^2c^{4\ }-\ 8a^2b^2c}{2a^2bc}  

a)

 3abc − 4abc3abc\ -\ 4abc  

b)

 3abc3 − 4b3abc^{3\ }-\ 4b  

c)

 3a3b2c4 − 4b3a^3b^2c^{4\ }-\ 4b  

d)

 3abc +4b3abc\ +4b  

14.

Simplify the expression. In your answer, use the carrot symbol for exponents. Example: For x2x^2 , type x^2

−45v4 + 9v3u + 9v2u29v2\frac{-45v^4\ +\ 9v^3u\ +\ 9v^2u^2}{9v^2}  

(a)  

15.
Simplify this expression.
Simplify this expression.
a)
5p2 - 16p
b)
5p + 4
c)
5p - 4
d)
5p + 4p
16.

 (x6y8−x4y6+x2y4)x2y2\frac{\left(x^6y^8-x^4y^6+x^2y^4\right)}{x^2y^2}  

a)

 x4y6−x2y4+y2x^4y^6-x^2y^4+y^2  

b)

 x3y4−x2y3+xy2x^3y^4-x^2y^3+xy^2  

c)

 x8y10−x6y8+x4y6x^8y^{10}-x^6y^8+x^4y^6  

d)

 0x4y6−0x2y4+0y20x^4y^6-0x^2y^4+0y^2  

17.
Question Image
a)
4y6
b)
4y22
c)
30y6
d)
30y22
18.

 20x25x\frac{20x^2}{5x}  

a)

 15x15x  

b)

 4x4x  

c)

 15x215x^2  

d)

 25x25x  

19.

 15mn2+30m3n4+45n55\frac{15mn^2+30m^3n^4+45n^5}{5}  

a)

 10mn2+25m3n4+40n510mn^2+25m^3n^4+40n^5  

b)

 20mn2+35m3n4+54n520mn^2+35m^3n^4+54n^5  

c)

 15mn2+6m3n4+45n515mn^2+6m^3n^4+45n^5  

d)

 3mn2+6m3n4+9n53mn^2+6m^3n^4+9n^5  

20.
Question Image
a)

2n2−12m+5mn3mn\frac{2n^2-12m+5mn^3}{mn}

b)

2n−12+5n22n-12+5n^2

c)

2n−12m+5mn2m\frac{2n-12m+5mn^2}{m}

21.
Use ^ to represent exponents and / to represent fractions. Ex: should be written as (x^2+y^3)/(x^4).

Use ^ to represent exponents and / to represent fractions. Ex: x2+y3x4\frac{x^2+y^3}{x^4} should be written as (x^2+y^3)/(x^4).

(a)  

WaygroundAnswer Key

dividing polynomials by monomials

Total questions: 21

1.
2k^2 + 5k - 4, 2k^2+5k-4
2.
a)

 x2−3y3x^2-3y^3  

3.
d) 4x4 - 9x2
4.
b) 3x6 - 8x3
5.
c)

 m+m5n2m+m^5n^2  

6.
d) 2x7 -2x -7
7.
a)

-3a + 6b

8.
c)

 2d−3d62d-3d^6  

9.
d)

divide, subtract

10.
a) 5w 2 − 4w + 3
11.
d)

5x65x^6  

12.
a) 5w 2 − 4w + 3
13.
b)

 3abc3 − 4b3abc^{3\ }-\ 4b  

14.
-5v^2 + vu + u^2, -5v^2+vu+u^2, -5v^2 + u^2 + vu, -5v^2+u^2+vu
15.
b) 5p + 4
16.
a)

 x4y6−x2y4+y2x^4y^6-x^2y^4+y^2  

17.
a) 4y6
18.
b)

 4x4x  

19.
d)

 3mn2+6m3n4+9n53mn^2+6m^3n^4+9n^5  

20.
a)

2n2−12m+5mn3mn\frac{2n^2-12m+5mn^3}{mn}

21.
(2+4y^2-8xy^4)/(xy), (2+4y^2-8xy^4)/xy, 2+4y^2-8xy^4/xy

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FAQs

What does this dividing polynomials by monomials worksheet cover?

This worksheet focuses on dividing each term of a polynomial by a monomial, including expressions with multiple variables and positive or negative terms. Its 21 items combine 3 fill-in-the-blank responses with 18 multiple-choice questions, requiring students to divide coefficients, subtract exponents variable by variable, and select or enter the resulting quotient.

How can I use this worksheet to teach dividing polynomials by monomials?

Model one multi-term example by showing that the monomial divisor applies to every term, then divide coefficients and subtract matching exponents in each term. Use the multiple-choice items to have students explain why distractors result from dividing only one term, adding exponents, or using the wrong coefficient; finish with the fill-in-the-blank items so students independently simplify and enter exponents with the caret symbol.

What mistakes should I watch for when students divide polynomials by monomials?

Watch for students dividing the divisor into only the first term instead of every term, or changing coefficients without applying the same operation across the polynomial. Common errors also include adding exponents instead of subtracting them, failing to subtract exponents for each variable, and losing a negative sign. In the fill-in-the-blank items, check that students use caret notation such as x^2 and preserve the complete simplified expression.

How do I assign and grade this dividing polynomials by monomials worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key for checking the 3 fill-in-the-blank and 18 multiple-choice responses, and printable student work can be graded by scanning it with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time.

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

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so multi-variable expressions and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet’s directions and question text into another language while students work through the polynomial-division items.

Where can I find more free 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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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