1Cademy - Factoring $$4x + 12$$

Learn Before

Factoring

Example

Factoring $4x + 12$

Factor $4x + 12$ by extracting the greatest common factor.

Step 1 — Find the GCF of $4x$ and $12$ : Factor each term into primes: $4x = 2 \cdot 2 \cdot x$ and $12 = 2 \cdot 2 \cdot 3$ . The common factors are two $2$ s, so $\text{GCF} = 2 \cdot 2 = 4$ .

Step 2 — Rewrite each term as a product of the GCF: Express $4x = 4 \cdot x$ and $12 = 4 \cdot 3$ , giving $4 \cdot x + 4 \cdot 3$ .

Step 3 — Apply the reverse Distributive Property: Factor out the $4$ : $4(x + 3)$ .

Step 4 — Check by multiplying: $4(x + 3) = 4 \cdot x + 4 \cdot 3 = 4x + 12$ ✓.

The factored form is $4(x + 3)$ .

Updated 2026-04-21

Contributors are:

Who are from:

References

OpenStax Elementary Algebra

Tags

OpenStax

Elementary Algebra @ OpenStax

Ch.7 Factoring - Elementary Algebra @ OpenStax

Algebra

Math

Prealgebra

Factoring the Greatest Common Factor from a Polynomial
Factoring $4x + 12$
Prime Polynomial
Factoring Trinomials of the Form $x^2 + bx + c$
Strategy to Factor Polynomials Completely
Identifying the Best Factoring Method for $6y^2 - 72$ , $r^2 - 10r - 24$ , and $p^2 + 5p + pq + 5q$
Factoring Special Products
Factoring Trinomials of the Form $ax^2 + bx + c$ Using Trial and Error
Factoring Trinomials of the Form $ax^2 + bx + c$ Using the ac Method
Solving a Quadratic Equation by Factoring
In a manufacturing facility, the total area of a rectangular storage zone is expressed as 6x^2 + 18x. To find the length and width, a technician performs a process that reverses multiplication to identify the original components, 6x and (x + 3). This process is known as ____.
In a professional setting, such as calculating the dimensions of a workspace or analyzing revenue streams, it is important to understand the relationship between mathematical operations. Match each term related to the decomposition of expressions with its correct description.
A logistics manager is reviewing the floor plan of a new distribution center. The total area is represented by a polynomial expression. To identify the individual dimensions (the length and the width) that were multiplied to result in that area, the manager needs to perform which mathematical operation?
In mathematical modeling and data analysis, the process of factoring is defined as breaking a product down into the original quantities that were multiplied together to produce it.
The Relationship Between Multiplication and Factoring
Project Cost Analysis
An operations analyst is studying a formula that represents the total daily output of a combined manufacturing unit. To identify the specific production rates of the individual components that were combined, the analyst applies the process of factoring. Arrange the following conceptual steps to correctly reflect the flow of factoring, beginning with the analyst's starting information.
Defining Factoring in Professional Applications
A production manager at a manufacturing plant is analyzing the total daily output, which is calculated by multiplying the 'Number of Machines' by the 'Units per Machine.' If the manager uses the process of factoring to break the total output back down into these two original variables, what is the mathematical term for the 'Number of Machines' and 'Units per Machine' in relation to the total product?
In professional data modeling, it is helpful to understand how mathematical operations relate to one another. Factoring is the process that 'undoes' or reverses multiplication. Which mathematical operation has a similar relationship with addition, acting as its reverse?
Factor as a Noun and a Verb
Factoring Trinomials of the Form $x^2 + bx + c$
Strategy for Factoring Trinomials of the Form $x^2 + bx + c$

Learn After

A logistics manager is simplifying a shipping cost formula represented by the expression 4x + 12. To ensure the formula is correctly simplified, arrange the steps for factoring 4x + 12 using the Greatest Common Factor (GCF) in the correct order.
An office supervisor is simplifying a supply cost formula represented by the expression 4x + 12. To factor this expression, the supervisor must first identify the Greatest Common Factor (GCF) of the two terms. The GCF of 4x and 12 is ____.
A project coordinator is simplifying a budget formula represented by the expression $4x + 12$. According to the standard factoring procedure for this specific expression, which of the following represents the correctly factored form using the Greatest Common Factor (GCF)?
An operations manager is simplifying a staff scheduling formula represented by the expression $4x + 12$. Match each part of the factoring process with its correct mathematical description.
Factoring in Procurement
A scheduling coordinator is simplifying a staff hour formula represented by the expression $4x + 12. True or False: The Greatest Common Factor (GCF) for this expression is 4, and its completely factored form is $4(x + 3).
Project Resource Allocation
Training Documentation: Simplifying Cost Formulas
An inventory manager is auditing a supply spreadsheet where the expression $4x + 12 $was simplified to \$ 4(x + 3)$ for better readability. To verify that both expressions represent the same total quantity, the manager uses a specific mathematical property to multiply the 4 by both the 'x' and the '3'. What is the name of this property?
A technical support specialist is following a maintenance manual to simplify a performance formula: $4x + 12. The manual lists the prime factors of each term as4x = 2 \cdot 2 \cdot x $and$ 12 = 2 \cdot 2 \cdot 3$. Based on these lists, which specific factors are identified as being 'common' to both terms?

Learn Before

Related

Learn After