Terms, Variables, Coefficients And Constants

In algebra, “terms,” “coefficients,” and “constants” are important concepts used to describe expressions and equations.

The following diagrams give examples of equations, expressions, terms, coefficients, variables, constants. Scroll down for examples and solutions.

Printable & Online Algebra Worksheets

Algebraic Expression Vocabulary - Terms, Coefficients, Constants

1. Terms
   A term is a single number, a variable, or numbers and variables multiplied together. Terms are separated by addition (+) or subtraction (-) signs.
   Examples:
   In the expression 3x + 7, “3x” is one term, and “7” is another term.
   In the expression 5y² - 2y + 9, “5y²”, “-2y”, and “9” are all separate terms.
   Single numbers like 8 or single variables like x are also terms.
   

2. Coefficients
   A coefficient is the numerical factor that is multiplied by a variable in a term. It’s the number that sits in front of the variable.
   Examples: In the term 3x, “3” is the coefficient. In the term -5y², “-5” is the coefficient. If a term is just a single variable like x, it’s understood to have a coefficient of 1 (because 1 * x = x).

3. Constants A constant is a term that has a fixed value. It’s a number on its own, without any variables attached. Its value doesn’t change. Examples: In the expression 3x + 7, “7” is the constant. In the expression 5y² - 2y + 9, “9” is the constant.

Example: Let’s look at the expression: 4x³ - 6x² + x - 2 Terms: The terms are 4x³, -6x², x, and -2. Coefficients: The coefficient of x³ is 4. The coefficient of x² is -6. The coefficient of x is 1 (because x is the same as 1x). Constant: The constant is -2.

Examples:

1. Consider the algebraic expression: 4x⁵ + ⁴ - 22x² - x + 17
   a. List the terms.
   b. Identify the constant term.

2. Complete the table by listing the factors and identifying the coefficients.

3. Consider the algebraic expression 5y⁴ - 8y³ + y² - y/4 - 7
   a. How many terms are there?
   b. Identify the constant term.
   c. What is the coefficient of the first term?
   d. What is the coefficient of the second term?
   e. What is the coefficient of the third term?
   f. List the factors of the fourth term.

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Terms And Coefficients
Defines terms and coefficients and variable part of a term in preparation for combining like terms.

A term is a number, variable, or a product or quotient of numbers and variables.

A variable expression contain one or more variable terms added or subtracted.

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Terms, Variables, Constants, Coefficients
A variable is a symbol (usually letter/letters) used to represent:
a) an unknown quantity (number)
b) any one of many numbers to indicate a general principle.

A constant is a single number.

A coefficient is a number “in front of” a variable.

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