## The Language of Factoring

Read this short article which provides an overview of the language and definitions you need to understand for factoring.

### Definitions: Product, Factors, Sum, Terms

A **product** is an expression where the last operation is **multiplication**. In a product, the things being multiplied are called the **factors**.

A **sum** is an expression where the last operation
is **addition**. In a sum, the things being added are called the **terms**.

1. For example, consider the expression .

If numbers are chosen for , , and , here is the order we would use to do the computations:

Notice that the **last** operation done is multiplication. Thus, the expression is a **product**.

2. As a second example, consider the expression .

Given numbers , , and , here is the order we would use to do the computations:

Notice that the **last** operation we do is addition. Thus, the expression is a **sum**.

Examples

1. The expression is a **product**.

The **factors** are **, , **

Note: The factors must be listed in order from left to right, and must be separated by commas.

2. The expression is a **product**.

The **factors** are **, , **

Note: Do not use parentheses when listing factors. In other words, do not put the inside parentheses.

3. The expression is a **sum**.

The **terms** are **, , **

Note: The terms must be listed in order from left to right, and must be separated by commas.

Remember that a term includes its sign.

4. The expression is a **sum**.

The **terms** are **, , **

Source: Tree of Math, https://www.onemathematicalcat.org/algebra_book/online_problems/prod_sum.htm

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