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Intro to Polynomials - Printable Math Worksheets class 8 - Wayground

Intro to Polynomials

Ashley Metzdorff

Created by Ashley Metzdorff

17 questions

8th Grade

Math

Updated Sept 2026

Intro to Polynomials is a Grade 8 mathematics worksheet that builds foundational skills for reading and classifying polynomials. Students identify a polynomial’s degree, classify expressions by number of terms as monomials, binomials, or trinomials, identify constants, recognize standard form, and rewrite expressions in descending powers. The worksheet includes 17 items: 15 multiple-choice questions, one multiple-select question, and one fill-in-the-blank question. Its varied question formats ask students to distinguish related polynomial features and apply classification rules to expressions with different terms and exponents. This free printable worksheet includes a complete answer key, making it useful for guided practice, independent work, or a formative check before students move to more advanced polynomial operations.

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Intro to Polynomials

Total questions: 17

Name
Class
Date
1.

Identify the degree of the polynomial

3x4 + 2x2 - 7

a)

1st degree

b)

2nd degree

c)

3rd degree

d)

4th degree

2.

Identify the degree of the polynomial

5x4 - 3x2 + 2x6 - x + 7

a)

2nd degree

b)

4th degree

c)

5th degree

d)

6th degree

3.

Identify the type of polynomial shown

2x2 + 3x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with more than 3 terms

4.

Identify the type of polynomial shown

5x2 + 7x - 2

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with more than 3 terms

5.

Identify the type of polynomial shown

-3

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial with more than 3 terms

6.
Classify by the number of terms:
4r6 - 3r2 - 8r4
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
7.
Classify by the number of terms:
2x5
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
8.
Classify by the number of terms:
10 + 8x
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
9.
Classify by the DEGREE:
3x - 2
a)
1
b)
2
c)
3
d)
4
10.
Classify
Classify
a)
Monomial
b)
Binomial
c)
Trinomial
d)
Polynomial
11.
Rewrite the polynomial in standard form: -5 + 4m
a)
-5 + 4m
b)
4m - 5
c)
-4m + 5
d)
4m2 - 5
12.
Classify by the DEGREE:
4x3 - 5x2 + 2x - 1
a)
1
b)
2
c)
3
d)
4
13.
What is the constant in the polynomial x2-2x+5?
a)
1
b)
2
c)
5
d)
0
14.

Which of these is in Standard Form? (check all that apply)

a)

 4x2+12x−13x34x^2+12x-13x^3  

b)

 5−3x5-3x  

c)

 2x4−12x2+5x−92x^4-12x^2+5x-9  

d)

 5x5+4x4+12x3−23x+155x^5+4x^{\text{4}}+12x^3-23x+15  

15.
The following polynomial is written in standard form:
7x3 - 11x2 + 8x - 5
a)
True
b)
False
16.

Which of the following polynomials is written in standard form?

a)

9 + 8x - 2x2

b)

10x + x3 - 4x2 - 11

c)

x4 + 5x3 - 6x +1

d)

4x3 + 3x4 + 2x + 1

17.

A polynomial is in (a)   form when it is in alphabetical order with exponents in decreasing order.

WaygroundAnswer Key

Intro to Polynomials

Total questions: 17

1.
d)

4th degree

2.
d)

6th degree

3.
b)

Binomial

4.
c)

Trinomial

5.
a)

Monomial

6.
c) Trinomial
7.
a) Monomial
8.
b) Binomial
9.
a) 1
10.
c) Trinomial
11.
b) 4m - 5
12.
c) 3
13.
c) 5
14.
c)

 2x4−12x2+5x−92x^4-12x^2+5x-9  

, d)

 5x5+4x4+12x3−23x+155x^5+4x^{\text{4}}+12x^3-23x+15  

15.
a) True
16.
c)

x4 + 5x3 - 6x +1

17.
standard

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FAQs

What does the Intro to Polynomials worksheet cover?

This Grade 8 worksheet practices identifying polynomial degree, classifying expressions by number of terms, finding the constant, and recognizing or rewriting polynomials in standard form. Its 17 items use multiple choice, multiple select, and fill-in-the-blank formats so students must apply these definitions to actual algebraic expressions rather than only recall vocabulary.

How can I use this worksheet to teach introductory polynomial concepts?

Begin by modeling how to count terms, locate the greatest exponent, identify the constant term, and arrange terms in descending powers. Then have students explain why an expression is a monomial, binomial, or trinomial before completing the multiple-choice items; use the standard-form and multiple-select questions to discuss why term order matters. Finish by reviewing the answer key and asking students to correct one classification or degree error in their own work.

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

Students may confuse the number of terms with the degree, such as calling an expression with three terms third degree, or may overlook the greatest exponent when terms are not already arranged. They may also identify the coefficient instead of the constant, arrange standard form in ascending order, or select an expression that is not fully ordered on the multiple-select item. Check that students treat a constant such as -3 as one term and carefully distinguish the degree from the number of terms.

How do I assign and grade this polynomial worksheet?

You can assign Intro to Polynomials as a printable PDF or as a digital quiz on Wayground, and it includes a complete answer key for grading. Printable submissions can also be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this polynomial worksheet for my students?

For the algebraic expressions and classification choices on this worksheet, use Advanced Settings to adjust font spacing or increase the font size for clearer visual separation of terms and exponents. You can also enable a dyslexia-friendly font or translate the worksheet into another language through Advanced Settings when those changes support access to the polynomial vocabulary and notation.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across 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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