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In algebra, the greatest common factor (GCF) is an important concept when factoring expressions. The GCF is the largest number or term that divides each term in an expression evenly.
Step 1 of the exercise asks us to identify the GCF of the terms in the expression. For the expression \(2x + 10\), we look at each term separately.
The terms are \(2x\) and \(10\). We need to find a common factor of both numbers. The number that divides both 2 and 10 is 2. Hence, the GCF here is 2.
Identifying the GCF simplifies the process of factoring complex expressions and helps to see patterns in algebraic manipulation.

The distributive property is a fundamental concept in algebra. It states that a term multiplied by a sum or difference inside parentheses can be distributed to each individual term within those parentheses:
For example, \(a(b + c) = ab + ac\).
In Step 3 of the exercise, we factor out the GCF using the distributive property. The expression after identifying the GCF is \(2x + 10\).
We rewrite this expression using the distributive property as: \(2(x + 5)\). By applying the distributive property in reverse, we confirm that \(2(x + 5) = 2 \times x + 2 \times 5\).
Recognizing and applying the distributive property correctly can make factoring and other algebraic processes more straightforward and accessible.

Algebra involves working with variables and constants to solve equations and manipulate expressions. Factoring is an essential technique in algebra that simplifies expressions and aids in solving equations.
In our exercise, we practiced factoring by identifying the common factor and applying the distributive property. These steps help break down algebraic expressions into simpler components.
The expression \(2x + 10\) was factored to \(2(x + 5)\) using algebraic principles. This process makes it easier to work with the expression in further algebraic operations like solving equations or simplifying larger expressions.
Understanding algebraic techniques such as factoring enhances problem-solving skills and builds a strong foundation for more advanced math topics.