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Operations on Polynomials - Printable Mathematics Worksheets - Wayground

Operations on Polynomials

20 questions

8th - 9th Grade

Mathematics

Operations on Polynomials is a Grade 8–9 Mathematics worksheet for Algebra I practice with 20 multiple-choice questions. Students classify polynomials by number of terms, add and subtract like terms, multiply binomials and polynomials, apply the distributive property, and simplify expressions involving exponents and powers of variables. The questions require students to track coefficients, signs, variable powers, and term order while selecting the equivalent simplified expression. This worksheet supports independent practice, guided review, or a short algebra skills check after instruction. Its varied multiple-choice items help teachers identify whether students are combining like terms accurately, distributing negative signs correctly, using exponent rules, and carrying out polynomial multiplication without losing terms. It is a free printable worksheet with an answer key, suitable for classroom practice, homework, intervention, or formative assessment.

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Operations on Polynomials

Total questions: 20

Name
Class
Date
1.
Classify by number of terms:
3x2 – 8x + 1
a)
Monomial
b)
Binomial
c)
Trinomial
d)
4-Term Polynomial
2.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
3.
Add the polynomials.
(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)
a)
4x3 + 1x2 – 3x + 1
b)
2x3 + 1x2 - 5x + 9
c)
6x3 + 1x - 1x2 - 3
d)
3x5 +1x - 1x5 - 3x
4.
Simplify each expression.
(6b3 + 6 - b4) - (8b3 - 6b4 + 2)
a)
4b4 - 2b3 + 7
b)
5b4 - 2b3 + 4
c)
b4 - 2b3 + 7
d)
5b4 - 2b3 + 7
5.
Find the product:
(3x – 1)(x + 5) 
a)
3x2 + 4x + 5
b)
3x2 + 4x - 5
c)
3x2 + 14x + 5
d)
3x2 + 14x - 5
6.
Simplify:
(3x - 5) ( 4x2 - 2x - 3)
a)
12x3 - 26x2 - 25x + 15
b)
12x3 - 20x2 - 5x + 15
c)
12x3 - 20x2 - 6x + 15
d)
12x3 - 26x2 + x + 15
7.
Find the sum.
(2x2 + 5x - 7) + ( 3 - 4x2 + 6x)
a)
2x2 + 3x +1
b)
-2x2 - 11x -4
c)
2x2 + 5x -7
d)
-2x2 + 11x -4
8.
Find the difference. 
(3- 2x + 2x2) - (4x -5 +3x2)
a)
x2 + 6x + 8
b)
2x2 + 5x - 7
c)
-x2 -6x + 8
d)
-2x2 + 11x - 4
9.
Simplify the expression.
x3(2x2+3x)
a)
2x5+3x4
b)
2x6+3x3
c)
5x9
d)
5x
10.
Find the difference.
(7p + 4p3 - 8) - (-3p2 + 2 - 9p)
a)
-3p2 + 4p3 -15 + 9
b)
3p3 + 4p2 - p + 3
c)
4p3 -3p2 +16p -10
d)
4p3 +3p2 + 16p + 10
11.
simplify 5x3 2x2
a)
10x5
b)
3x
c)
10x6
d)
7x5
12.
Simplify the following:
(x2y)5
a)
x7y5
b)
x2y5
c)
x10y5
d)
x5y5
13.
Simplify the exponential expression.
a)
2x6y12
b)
2x5y7
c)
8x6y12
d)
8x5y7
14.

Simplify the expression

a)

x2/2

b)

2/x14

c)

2x14

d)

2/x2

15.
a)
2a2b6
b)
1/2a2b6
c)
b6/2a2
d)
2b6/a2
16.
Simplify the expression.
-3x2( 7x2 - x + 4)
a)
-21x4 + 3x3 -12x2
b)
7x2 - x + 4 (-3x2)
c)
21x4 + 3x3 + 12x2
d)
-12x2 + 3x3 -21x4
17.

Find the product:

(2x + 7)2

a)

4x2 + 49

b)

4x2 + 28x + 49

c)

4x2 + 14x + 49

18.
Simplify:
(3x - 5) ( 4x2 - 2x - 3)
a)
12x3 - 26x2 - 25x + 15
b)
12x3 - 20x2 - 5x + 15
c)
12x3 - 20x2 - 6x + 15
d)
12x3 - 26x2 + x + 15
19.
Find the product:
(5n-8)(5n+8)
a)
25n2-64
b)
10n2
c)
5n2+16
d)
16
20.
Find the product:
(3r-4)(7r-5)
a)
21r2-43r+20
b)
21r+43r2+9
c)
7r+12r
d)
r+2r
Answer Key

Operations on Polynomials

Total questions: 20

1.
c) Trinomial
2.
d) -2x2 + 11x -4
3.
a) 4x3 + 1x2 – 3x + 1
4.
b) 5b4 - 2b3 + 4
5.
d) 3x2 + 14x - 5
6.
d) 12x3 - 26x2 + x + 15
7.
d) -2x2 + 11x -4
8.
c) -x2 -6x + 8
9.
a) 2x5+3x4
10.
c) 4p3 -3p2 +16p -10
11.
a) 10x5
12.
c) x10y5
13.
c) 8x6y12
14.
c)

2x14

15.
c) b6/2a2
16.
a) -21x4 + 3x3 -12x2
17.
b)

4x2 + 28x + 49

18.
d) 12x3 - 26x2 + x + 15
19.
a) 25n2-64
20.
a) 21r2-43r+20

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FAQs

What does the Operations on Polynomials worksheet cover?

This Grade 8–9 Algebra I worksheet uses 20 multiple-choice questions to assess polynomial classification, addition, subtraction, multiplication, distribution, and exponent simplification. Students select equivalent expressions such as combined polynomials, expanded products, and correctly simplified powers, building accuracy with coefficients, signs, like terms, and variable exponents.

How can I use this worksheet to teach operations on polynomials?

Use the questions in a progression: begin with classifying terms and combining like terms, then model subtraction by distributing the negative sign before moving to polynomial products. Have students explain why each term in a product must be multiplied and which exponent rule supports each power-simplification item. Pause after selected multiple-choice questions to compare the correct expression with distractors created by sign, coefficient, or exponent errors.

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

Watch for students combining unlike terms, changing only some signs when subtracting a polynomial, or omitting a product when expanding a binomial or larger polynomial. In the exponent items, students may add exponents when they should multiply powers, multiply coefficients incorrectly, or confuse a product such as x³(2x² + 3x) with a single-term expression. The multiple-choice distractors make these errors visible for review.

How do I assign and grade this Operations on Polynomials worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the 20 multiple-choice questions. For printable submissions, teachers can scan student work with the Wayground for Teachers app to grade it efficiently.

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

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the polynomial expressions and answer choices easier to scan. You can also enable a dyslexia-friendly font or translate the written directions into another language while keeping the algebraic notation clear.

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 support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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