Reading the Parts of
an Expression

Break down any algebraic expression into its terms, factors, and coefficients — and read each piece with confidence.

Algebra 2

Why Structure Matters

An expression like $ 3x^2 + 5x - 8 $ is not just a string of symbols. It is built from organized pieces, each with its own name and role.

Three Words to Know

Term

A single piece separated by $ + $ or $ - $ signs.

Factor

A quantity being multiplied within a term.

Coefficient

The number multiplied by the variable in a term.

Anatomy of an Expression

What Is a Term?

A term is a part of an expression that is added or subtracted. The $ + $ and $ - $ signs are the "fences" that divide an expression into terms.

What Is a Factor?

A factor is any quantity being multiplied inside a single term. A term can have several factors.

What Is a Coefficient?

A coefficient is the numerical factor multiplying the variable part of a term. When you see a variable with "no number," its coefficient is $ 1 $.

The Structure Rule

Any polynomial term can be written as:

$$ \underbrace{a}_{\text{coefficient}} \cdot \underbrace{x^n}_{\text{variable factor}} $$

Term vs. Factor

These are easy to confuse — the operation between pieces tells them apart.

	Terms	Factors
Separated by	$ + $ and $ - $	multiplication
In $ 3x + 5 $	$ 3x $, $ 5 $	—
In $ 3x $	one term	$ 3 $, $ x $
Combine by	adding like terms	multiplying

How to Break It Down

1

Split into terms. Cut the expression at every $ + $ and $ - $ sign.

2

Attach the sign. Keep each term's leading $ + $ or $ - $ with it.

3

Find the factors. List the quantities multiplied inside each term.

4

Name the coefficient. Identify the numerical factor (use $ 1 $ if none is shown).

Example 1: Simple

Analyze $ 4x + 7 $.

Example 2: Three Terms

Analyze $ 2x^2 - 5x + 9 $.

Example 3: Real-World

A profit model is $ P = 15n - 200 $, where $ n $ is items sold.

Common Mistakes

✕ Dropping the sign

In $ 3x - 7 $, the second term is $ -7 $, not $ 7 $. The minus belongs to the term.

✕ Forgetting coefficient 1

The coefficient of $ x $ (alone) is $ 1 $, and of $ -x $ is $ -1 $.

✕ Mixing terms and factors

$ 6xy $ is one term with factors $ 6, x, y $ — not three separate terms.

Quick Reference

Part	Defined By	Example in $ 5x^2 - 3x $
Term	add / subtract	$ 5x^2 $, $ -3x $
Factor	multiplication	$ 5, x, x $ in first term
Coefficient	numeric factor	$ 5 $ and $ -3 $
Constant	no variable	none here

Question 1 of 5

How many terms are in $ 4x^2 - 7x + 2 $?

The expression splits at each $ + $ and $ - $ into $ 4x^2 $, $ -7x $, and $ 2 $: three terms.

Question 2 of 5

What is the coefficient of $ x $ in $ 9 - 6x $?

The term is $ -6x $, so the coefficient — including its sign — is $ -6 $.

Question 3 of 5

Which lists the factors of the term $ 8ab $?

$ 8ab $ is one term that is the product of the factors $ 8 $, $ a $, and $ b $.

Question 4 of 5

In $ x^2 + x - 5 $, what is the coefficient of the $ x $ term?

A variable written alone has an understood coefficient of $ 1 $: the term $ x $ means $ 1x $.

Question 5 of 5

In the cost model $ C = 12h + 50 $, what does the constant term $ 50 $ represent?

The constant $ 50 $ does not change with $ h $, so it represents a fixed cost. The coefficient $ 12 $ is the per-hour rate.

	Terms	Factors
Separated by	\( + \) and \( - \)	multiplication
In \( 3x + 5 \)	\( 3x \), \( 5 \)	—
In \( 3x \)	one term	\( 3 \), \( x \)
Combine by	adding like terms	multiplying

Part	Defined By	Example in \( 5x^2 - 3x \)
Term	add / subtract	\( 5x^2 \), \( -3x \)
Factor	multiplication	\( 5, x, x \) in first term
Coefficient	numeric factor	\( 5 \) and \( -3 \)
Constant	no variable	none here

Reading the Parts of an Expression

Why Structure Matters

Three Words to Know

Anatomy of an Expression

What Is a Term?

What Is a Factor?

What Is a Coefficient?

The Structure Rule

Term vs. Factor

How to Break It Down

Example 1: Simple

Example 2: Three Terms

Example 3: Real-World

Common Mistakes

Quick Reference

Question 1 of 5

Question 2 of 5

Question 3 of 5

Question 4 of 5

Question 5 of 5

Reading the Parts of
an Expression