Worksheets · Algebra 1

Naming polynomials worksheet for Algebra 1

Two labels on every polynomial: what its highest power is, and how many terms it has. Half the questions also ask for standard form and the leading coefficient, so the terms have to be put in order first.

Also taught in Algebra 2, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Naming Polynomials

Date Period

Name each polynomial, or answer as asked.

  1. Name by degree and number of terms

    −9a2+7a+3
  2. 8
  3. −3
  4. 3y2+9
  5. 3x2−5
  6. −4m3+8m−8
  7. −7x3+5x2+3x−2
  8. −m2+5
  9. a2−9a
  10. v3−8v2−7v+1

  1. Write in standard form and classify

    Write in standard form, name it, and give the leading coefficient: −4−5x2
  2. Write in standard form, name it, and give the leading coefficient: −7x2−7x3
  3. Write in standard form, name it, and give the leading coefficient: −x3
  4. Write in standard form, name it, and give the leading coefficient: 9x4
  5. Write in standard form, name it, and give the leading coefficient: −9x2
  6. Write in standard form, name it, and give the leading coefficient: 9−3x−3x2
  7. Write in standard form, name it, and give the leading coefficient: x2−4−6x3
  8. Write in standard form, name it, and give the leading coefficient: −1+9x2
  9. Write in standard form, name it, and give the leading coefficient: −9x+2x3
  10. Write in standard form, name it, and give the leading coefficient: 4+5x+8x2

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Naming PolynomialsAnswer keyVersion 1

Date Period

Name each polynomial, or answer as asked.

  1. Name by degree and number of terms

    −9a2+7a+3Quadratic trinomial
  2. 8Constant monomial
  3. −3Constant monomial
  4. 3y2+9Quadratic binomial
  5. 3x2−5Quadratic binomial
  6. −4m3+8m−8Cubic trinomial
  7. −7x3+5x2+3x−2Cubic polynomial with 4 terms
  8. −m2+5Quadratic binomial
  9. a2−9aQuadratic binomial
  10. v3−8v2−7v+1Cubic polynomial with 4 terms

  1. Write in standard form and classify

    Write in standard form, name it, and give the leading coefficient: −4−5x2−5x2−4; quadratic binomial; leading coefficient −5
  2. Write in standard form, name it, and give the leading coefficient: −7x2−7x3−7x3−7x2; cubic binomial; leading coefficient −7
  3. Write in standard form, name it, and give the leading coefficient: −x3−x3; cubic monomial; leading coefficient −1
  4. Write in standard form, name it, and give the leading coefficient: 9x49x4; quartic monomial; leading coefficient 9
  5. Write in standard form, name it, and give the leading coefficient: −9x2−9x2; quadratic monomial; leading coefficient −9
  6. Write in standard form, name it, and give the leading coefficient: 9−3x−3x2−3x2−3x+9; quadratic trinomial; leading coefficient −3
  7. Write in standard form, name it, and give the leading coefficient: x2−4−6x3−6x3+x2−4; cubic trinomial; leading coefficient −6
  8. Write in standard form, name it, and give the leading coefficient: −1+9x29x2−1; quadratic binomial; leading coefficient 9
  9. Write in standard form, name it, and give the leading coefficient: −9x+2x32x3−9x; cubic binomial; leading coefficient 2
  10. Write in standard form, name it, and give the leading coefficient: 4+5x+8x28x2+5x+4; quadratic trinomial; leading coefficient 8

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

4x2−7x+1

  1. The highest power is 2, so it is quadratic.
  2. Count the terms: three of them.

The answer is Quadratictrinomial.

Where students go wrong

Counting the degree from the number of terms, or the other way round. They are independent: x⁵ - 2 is a quintic binomial, with a high degree and only two terms. Read the highest power for one and count for the other.

Also called classifying polynomials, degree of a polynomial or monomial binomial trinomial.

What you can put on this worksheet

Name by degree and number of terms
−9v−6 → Linear binomial
Standard form and the leading coefficient
Write in standard form, name it, and give the leading coefficient: 3x2−5x3 → −5x3+3x2; cubic binomial; leading coefficient −5
6th and 7th degree, terms out of order
8k4+5k3+k+6k6 → 6th degree polynomial with 4 terms

Questions about these worksheets

Yes. Every naming polynomials sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the naming polynomials questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 3: name by degree and number of terms, standard form and the leading coefficient and 6th and 7th degree, terms out of order. Tick as many as you want and set how many of each, or let it spread them evenly.

Counting the degree from the number of terms, or the other way round. They are independent: x⁵ - 2 is a quintic binomial, with a high degree and only two terms. Read the highest power for one and count for the other.