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Factoring
Factoring is the process of breaking a product down into the quantities that were multiplied together to produce it — the reverse of multiplication. When multiplying, two or more factors are combined to form a product; when factoring, a product is decomposed back into its factors. For example, multiplying and gives , while factoring recovers the original factors and . Similarly, multiplying produces , while factoring can recover and (among other factor pairs). Factoring undoes the work of multiplication, much like subtraction undoes addition.
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Elementary Algebra @ OpenStax
Ch.7 Factoring - Elementary Algebra @ OpenStax
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Intermediate Algebra @ OpenStax
Ch.6 Factoring - Intermediate Algebra @ OpenStax
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Prime Number
Factoring
Greatest Common Factor
A warehouse manager is organizing 48 items into equal-sized boxes. If the manager uses 4 boxes with 12 items each (4 * 12 = 48), what is the mathematical term for the numbers 4 and 12 in relation to the total 48?
A payroll specialist notes that an employee worked 8 hours a day for 5 days, totaling 40 hours. In the mathematical relationship 8 * 5 = 40, the numbers 8 and 5 are called ____ of 40.
A project manager determines that a team of 6 employees working 40 hours each will contribute a total of 240 labor hours (6 * 40 = 240). In this mathematical relationship, the numbers 6 and 40 are defined as factors of 240.
A department manager calculates that a team of 12 employees working 5 hours each contributes 60 total labor hours (12 × 5 = 60). Match each component of this scenario to its correct mathematical description based on the concept of factors.
Identifying Factors in Warehouse Logistics
A project coordinator is explaining the 'Factor Rule' to a new team member using the example of a 40-hour work week ($8 \text{ hours/day} \times 5 \text{ days} = 40 \text{ total hours}$). Arrange the following statements in the correct logical sequence to define why 8 and 5 are factors of 40 according to the course definition.
Solar Array Configuration
Defining Factors in a Professional Context
A logistics coordinator is arranging 24 pallets in a warehouse into equal-sized rows. To determine all possible configurations for the display, the coordinator must identify all factors of 24. Which of the following is the complete list of factors for the number 24?
In a resource allocation report, if 20 is identified as a factor of 100, then according to the course definition, 100 is mathematically defined as a ________ of 20.
Finding All the Factors of
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Factoring the Greatest Common Factor from a Polynomial
Factoring
Factoring
Prime Polynomial
Factoring Trinomials of the Form
Strategy to Factor Polynomials Completely
Identifying the Best Factoring Method for , , and
Factoring Special Products
Factoring Trinomials of the Form Using Trial and Error
Factoring Trinomials of the Form 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
Strategy for Factoring Trinomials of the Form