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In algebra, the *Greatest Common Factor* (GCF) is the largest number that evenly divides two or more coefficients. To identify the GCF, we look at the terms in the expression we wish to factor. For example, consider the expression \(-20x - 10\).
First, separate the coefficients of each term. Here, the coefficients are -20 and -10.
To find the GCF, list the factors of each coefficient:

• Factors of -20 are: 1, 2, 4, 5, 10, and 20.
• Factors of -10 are: 1, 2, 5, and 10.

The common factors are 1, 2, 5, and 10.
The largest common factor is 10, so the GCF of -20 and -10 is 10. This means 10 is the largest number that divides both -20 and -10 without leaving a remainder. Identifying the GCF is an essential first step in factoring any algebraic expression. It simplifies the problem and makes the next steps, like factoring out the GCF, easier.

Factoring is crucial for simplifying algebraic expressions and solving equations. Once the *Greatest Common Factor* (GCF) has been identified, it's time to factor out the GCF from the expression. For example, if we have \(-20x - 10\) and already know that the GCF is 10, we proceed as follows:
Divide each term in the expression by the GCF (10) to isolate the simplified terms inside parentheses:
\begin{align*}-20x ÷ 10 &= -2x\-10 ÷ 10 &= -1\frac{{Cconst}\

• Write the GCF outside and the simplified terms inside the parentheses: 10(–2x - 1)

This is the factored form of the original expression \(-20x - 10\).
This method can be applied to more complex expressions, making it a versatile technique in algebra.
Remember, factoring makes expressions simpler and is often the first step in solving equations.

Understanding basic *algebraic operations* is crucial for factoring expressions.
Operations like addition, subtraction, multiplication, and division are foundational. They allow us to manipulate algebraic expressions effectively.
Let's revise these operations:

• *Addition/Subtraction* involves combining like terms. For example, in \(5x + 3x\), we add the coefficients of \(x\), resulting in \(8x\).
• *Multiplication* often involves applying the distributive property, like in \(3(x + 4)\), giving us \(3x + 12\).
• *Division* helps in finding the GCF and simplifying expressions, as seen in factoring \(-20x - 10\) by 10.

Each algebraic operation follows specific rules. Mastering these rules simplifies more complex tasks like factoring and solving equations. It's the bedrock upon which more advanced algebraic techniques are built.