Polynomial Vocabulary Worksheet – Terms, Degree, Roots

All 36 terms

Terms and degree 12

coefficient The numerical factor of a term. In 7x³ the coefficient is 7.
constant term The term that has no variable in it. In x² + 6x + 9 the constant term is 9.
degree The largest power of x found among the terms. 7x⁴ − 2x has degree 4.
distributive property The rule that a(b + c) equals ab + ac. 5(x − 2) = 5x − 10.
exponent The raised number that shows a power of the base. In x³ the exponent is 3.
expression Numbers and letters joined by signs, with no equals sign. 2x + 1 is an expression; it has no equals sign.
indeterminate A symbol in a polynomial that stands for no fixed value. In x² + 1 the indeterminate is x.
leading coefficient The number that multiplies the highest power of x. In 7x⁴ − 2x the leading coefficient is 7.
like terms Terms whose variable parts match exactly. 3x² and −5x² are like terms.
polynomial A sum of terms built from numbers and powers of variables. 3x² + 2x − 5 is a polynomial.
term One of the pieces of an expression joined by + or −. The terms of 3x² + 2x − 5 are 3x², 2x and −5.
zero polynomial The polynomial whose every coefficient is 0. Its degree is left undefined or taken as negative.

Show all 36 terms (24 more)

Kinds of polynomial 12

binomial An expression of two unlike terms, added or subtracted. x + 3 is a binomial.
constant polynomial A polynomial that is a single number, such as 7. Its degree is 0, unless the number is 0 itself.
cubic Having degree 3: the highest power is a cube. x³ − 8 is cubic.
linear Having degree 1: no power of x above the first. 2x + 1 is linear.
monic Having a leading coefficient of 1. x² + 3x is monic; 2x² + 3x is not.
monomial An expression with a single term. 5x² is a monomial.
multivariate Having two or more variables. x² + xy + y² is multivariate.
quadratic Having degree 2: the highest power is a square. x² − 4x + 4 is quadratic.
quartic Having degree 4. x⁴ + x² is quartic.
quintic Having degree 5. x⁵ − x is quintic.
trinomial Three unlike terms joined by plus or minus signs. x² + 2x + 1 is a trinomial.
univariate Having only one variable. x² + 3x is univariate.

Roots and division 12

dividend The expression that is being divided. In (x² − 1) ÷ (x − 1) the dividend is x² − 1.
divisor The expression that another is divided by. In (x² − 1) ÷ (x − 1) the divisor is x − 1.
factorization The same polynomial written as factors multiplied together. x² − 4 = (x − 2)(x + 2).
fundamental theorem of algebra Says a polynomial that is not constant has a complex root. So a polynomial of degree 3 has three complex roots, counted with multiplicity.
long division Division worked out in full, one step after another. Polynomials can be divided by long division, as whole numbers can.
multiplicity The number of times one root is repeated. In (x − 3)² the root 3 has multiplicity 2.
quadratic formula The formula for the roots of any quadratic equation. It gives the roots of ax² + bx + c = 0 from a, b and c.
rational function A function written as one polynomial over another. 1/x is a rational function.
remainder theorem Says dividing p(x) by x − c leaves the remainder p(c). Dividing x² + 1 by x − 2 leaves 5, and 2² + 1 = 5.
root A number that gives 0 when put in place of x. 2 is a root of x² − 4. A root is also called a zero.
synthetic division A shortcut for dividing a polynomial by x minus a number. It works with the coefficients alone.
x-intercept A point where the curve of a graph touches the x-axis. The graph of x² − 4 has x-intercepts at −2 and 2.

How this list was compiled: Term list chosen for this site on 2026-10-02. Each meaning is written in our own words and was checked that day against the entry for the term in Wiktionary, the free dictionary (https://en.wiktionary.org/), whose text is under the Creative Commons Attribution-ShareAlike license, and, for the terms with no entry of their own (leading coefficient, distributive property, constant polynomial, zero polynomial, remainder theorem, fundamental theorem of algebra), against the articles Polynomial, Coefficient and Distributive property in English Wikipedia (https://en.wikipedia.org/), whose text is under the Creative Commons Attribution-ShareAlike license. Every example is our own working. The example after each meaning is our own. Licence: own work

How it works

This polynomial vocabulary worksheet prints twelve terms down the left and their meanings, mixed up, down the right. Three sets cover terms and degree, the kinds of polynomial, and roots and division.

Read the full guide

Three sets

Set opens on Terms and degree: polynomial, term, coefficient, degree, constant term, leading coefficient and like terms. Kinds of polynomial runs from monomial to quintic, monic and multivariate. Roots and division adds root, multiplicity, synthetic division and the remainder theorem.

A worked line under every meaning

Under the tool each term is shown at work. Degree: 7x⁴ − 2x has degree 4. Multiplicity: in (x − 3)² the root 3 has multiplicity 2. Your own term = meaning lines, typed in the box, replace ours.

The third set names two theorems.

Questions and answers

What is the degree of a polynomial?

It is the highest exponent of the variable. 7x⁴ − 2x has degree 4. A nonzero constant such as 7 has degree 0, and the degree of the zero polynomial is left undefined or taken as negative.

What is the difference between a monomial, a binomial and a trinomial?

The number of terms. A monomial has exactly one term, such as 5x². A binomial has two, such as x + 3, and a trinomial has three, such as x² + 2x + 1.

Is there a polynomial vocabulary worksheet PDF?

There is no PDF button. Press Print worksheet and choose Save as PDF in your browser's print window; the key is saved as its last page.

Where is the answer key?

It prints after the sheet as one more page, with a line drawn from each term to its meaning. See the answers, under More options, draws the same lines on screen.