Factor out the greatest common factor. $18x+27$

Verified step by step guidance

1. Identify the greatest common factor (GCF) of the coefficients 18 and 27. To do this, find the largest number that divides both 18 and 27 evenly.
2. Determine if there is a common variable factor in the terms. Since the terms are 18x and 27, check if both terms contain the variable 'x'.
3. Write the GCF based on the common numerical factor and any common variable factors found. In this case, it will be a number since only one term has 'x'.
4. Express each term as a product of the GCF and another factor. For example, write 18x as (GCF) times something, and 27 as (GCF) times something else.
5. Factor out the GCF from the entire expression and write the factored form as \(\text{GCF} \left( \text{remaining factor of first term} + \text{remaining factor of second term} \right)\).

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest factor that divides two or more numbers or expressions without leaving a remainder. Finding the GCF helps simplify expressions by factoring out common terms, making further operations easier.

Factoring Out the GCF

Factoring out the GCF involves rewriting an expression as a product of the GCF and another simplified expression. This process reduces the expression to a simpler form and is often the first step in factoring polynomials.

Factoring Algebraic Expressions

Factoring algebraic expressions means expressing them as a product of simpler expressions. Recognizing common factors, such as numbers and variables with the smallest exponents, is essential to break down expressions effectively.