© 2016 Shmoop University, Inc. All rights reserved.

Polynomials Terms

Get down with the lingo

Algebraic Expressions

An expression that contains one or more terms and operations to combine them. Each term contains variable(s), constant(s), or a product of variables and constants.


A polynomial with only two terms. The expression x – 3 is a binomial, and so is 96x2y + 13,0278,543.


The number being multiplied by a variable. Coefficients give regular old variables a little boost! For example, the coefficient in 3x is 3.


A value that doesn't change. In a polynomial, the constant is the number that's not being multiplied by a variable, like the 4 in x2 + 11x + 4.

Degree Of A Polynomial

The largest combined exponent value of any one term in that polynomial. For example, the degree of the polynomial 7x9 – 2x5y6 is 11. It also has a Ph.D. in Italian literature. Go figure.

Descending Order

Greatest to least. In a polynomial, we usually write the terms starting with the highest exponent first, and the lowest (or the constant) last.

Difference Of Two Squares

An expression that takes the form a2b2 that we can factor into the form (a + b)(ab).


Mathematical "sentences" that state the equality of two algebraic expressions.

Equivalent Equations

Two different pairs of equations that have the same solution(s).


Breaking a polynomial into two or more expressions that can be multiplied together to get the original polynomial. Basically, it's like reverse-distributing.

Like Terms

Two terms that have the same variables raised to the same exponent. Like terms may have different coefficients.


A polynomial that's just a single term, like 5x or -16xy2z. Aww, it's so widdle and cute.

Multivariable Polynomials

Polynomials with more than one variable. These guys like to mix it up.


An expression containing constants and variables that can be combined using addition, subtraction, and multiplication. Exponents on all variables must be positive whole numbers.

Prime Polynomial

Lke a prime number or Optimus Prime, prime polynomials can't be broken down any further by factoring. A prime polynomial's only factors are 1 and itself.

Quadratic Polynomials

A polynomial of degree 2.


The value(s) of variable(s) that satisfy an equation or inequality.


A polynomial with three terms. Third time's a charm.


A value that changes. Variables are commonly represented by the letters x, y, or z.

People who Shmooped this also Shmooped...