6E Parts of an Expression Study Guide

Key Vocabulary

Term — a part of an expression separated by + or − signs. (término)

Coefficient — the number in front of (multiplied by) a variable. (coeficiente)

Constant — a term that is just a number (no variable). (constante)

Variable — a letter that represents an unknown number. (variable)

Exponent — the small number above and to the right of a base that tells how many times to multiply. (exponente)

Labeled Expression Diagram

Look at the expression 3x² + 5x − 7 and identify each part:

coefficient 3 variable x exponent ² + coefficient 5 variable x − constant 7

This expression has 3 terms:
• 3x² — first term (coefficient = 3, variable = x, exponent = 2)
• 5x — second term (coefficient = 5, variable = x, exponent = 1)
• −7 — third term (constant — no variable)

Step-by-Step: Identifying Parts

1 Find the terms. Split the expression at each + or − sign. Each piece is a term.
2 Find the coefficient of each term. It is the number in front of the variable. If there is no number, the coefficient is 1.
3 Find the variable(s). These are the letters.
4 Find the exponent. It is the small raised number. If there is no exponent shown, it is 1.
5 Find constants. These are terms with no variable attached.

Example: In the expression 8y − 3:
• Terms: 8y and −3
• Coefficient of y: 8
• Variable: y
• Constant: −3

Quick Reference

Term = a piece of an expression separated by + or −

Coefficient = number in front of the variable
Constant = number with NO variable
Exponent = power (how many times to multiply)

Watch Out!

If a variable has no number in front, the coefficient is 1. x means 1x.
The sign belongs to the term. In 4x − 9, the constant is −9 (negative 9), not just 9.
Exponents are NOT coefficients. In 3x², the 3 is the coefficient and the 2 is the exponent. They do different things.
A constant IS a term. The number 5 by itself is a term with coefficient 0 for any variable (or just a standalone number).

Practice Problems

1. In the expression 6x + 4, what is the coefficient of x?

2. In the expression 2y² − 3y + 10, how many terms are there?

3. In the expression 9m + 5, what is the constant?