Vocabulary for Working with Algebraic Expressions

If you want to really understand algebra and do well in math, then you need to be fluent in the language of math. There are some vocabulary words that math people will throw around, and if you don't understand them... you're going to be lost!

So here are four basic words that you need to know when talking about algebraic expressions.

What Is a Coefficient? What Are Coefficients?

A coefficient is a constant number, like "-1" or "7." A coefficient is usually attached to a variable, as in "2x," where "x" is the variable and "2" is the coefficient.

What Is a Variable? What Are Variables?

A variable is a symbol (usually a letter) that represents an unknown quantity. If you're talking about "4x," then "x" is the variable. It's an unknown quantity in the expression, and the "x" serves as a placeholder. Note that the constant number in front, "4" is a coefficient like we defined above.

What Is a Term? What Are Terms?

A term is a combination of a coefficient and a variable. For example, "8y," taken as a whole, is a term. It's made up of a coefficient (8) and a variable (y). "12xyz" is a more complicated term; it includes a coefficient (12) and three variables (x, y, and z).

What Is a Polynomial? What Are Polynomials?

A polynomial is a collection of terms, related by addition or substraction. For example, "x^2 + 4x + 4" is a polynomial. Notice that the polynomial has three terms. "x^2" is a term (which consists of a variable and, technically, a coefficient of 1). "4x" is another term (made up of a coefficient, "4", and a variable, "x"). "4" is the final term, and it consists of nothing but a coefficient ("4").

You can be more specific, and use words that indicate how many terms are in a polynomial. The earlier example (x^2 + 4x + 4) is a trinomial, because it consists of three terms. The polynomial "4x + 8y" is a binomial, because it consists of two terms. A single term, like "12xy^2" is called a monomial.

Within a polynomial, there are also special kinds of coefficients and terms. The leading term is the first term in the polynomial. In the polynomial "8x^2 + 4x + 12," the leading term is "8x^2." The leading coefficient is the leading coefficient of that first term - in this case, the number 8.