Decode Expressions: Terms, Factors & Coefficients

In Algebra 1, you're expected to read an expression like a sentence and identify what each part does. Most test questions ask you to name the terms, spot factors, and identify coefficients so you can simplify, combine like terms, or interpret a situation.

Mental model: "Add vs. Multiply"

Expressions are built from two main operations:

1. Addition/Subtraction → Terms

2. Multiplication/Division → Factors

If you can tell whether parts are being added or multiplied, you can label the structure correctly.

As shown in Figure 1, terms are separated by +/−, while factors are the pieces being multiplied inside each term.

Key definitions (what to identify)

• Expression: A math phrase without an equals sign (e.g., $3x-5+2x^2$).
• Term: A chunk separated by $+$ or $-$ at the "top level."
  • Example: In $4x^2-3x+7$, the terms are $4x^2$, $-3x$, and $7$.
  • A leading minus belongs to the term: $-3x$ is one term.
• Factor: Quantities that are multiplied to make a term.
  • Example: In $-3x$, the factors are $-3$ and $x$.
  • Parentheses often show factors: $2(x-5)$ has factors $2$ and $(x-5)$.
• Coefficient: The numerical factor multiplying the variable part.
  • Example: In $-3x$, the coefficient is $-3$.
  • In $x$ (meaning $1x$), the coefficient is 1. In $-x$, it's −1.
• Constant term: A term with no variable (e.g., $7$).

What you do not need here (out of scope)

• You do not need to factor polynomials fully (like $x^2+5x+6=(x+2)(x+3)$) for this skill.
• You do not need exponent rules beyond recognizing that $x^2$ is part of a term.
• You do not need to solve equations—this is about interpreting parts of an expression.