Learn Before
Identifying the Best Factoring Method for , , and
Identify the best factoring method for each polynomial by applying the preliminary factoring strategy.
ⓐ
- Is there a GCF? Yes, the GCF is 6. Factor it out: .
- What type of polynomial remains? The expression is a binomial. There is currently no method available for factoring this binomial, so the factoring is complete.
ⓑ
- Is there a GCF? No, the three terms share no common factor.
- What type of polynomial is it? It is a trinomial with a leading coefficient of 1, so the appropriate method is to "undo" FOIL — find two numbers whose product is and whose sum is .
ⓒ
- Is there a GCF? No, all four terms share no single common factor.
- What type of polynomial is it? It has more than three terms (four terms), so the appropriate method is factoring by grouping.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.7 Factoring - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
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
Learn After
In a business logistics analysis, different cost functions are represented by polynomials. Match each polynomial expression with the correct initial factoring strategy used to simplify it.
An inventory specialist uses the expression to model stock fluctuations. According to the standard factoring strategy for a trinomial with a leading coefficient of 1, which step should be taken to factor this expression?
A logistics coordinator is analyzing a shipment volume model represented by the polynomial . Because this expression consists of four distinct terms and has no common factor for all terms, the standard factoring strategy identifies factoring by ________ as the most appropriate technique to apply.
A manufacturing analyst is simplifying a cost function represented by $6y^2 - 72. True or False: According to the standard preliminary factoring strategy, after factoring out the Greatest Common Factor (GCF) of 6, the resulting expression $6(y^2 - 12) is considered fully factored because no further factoring methods apply to the binomial .
A business analyst is using the preliminary factoring strategy to simplify various financial models. Arrange the following diagnostic steps in the correct sequence to identify the best factoring method for any polynomial expression.
Factoring Strategies for Logistics Optimization
Factoring Requirements for Trinomial Logistics Models
Internal Documentation: Standard Factoring Strategy for Algebraic Models
An inventory specialist is using the expression to model fluctuations in warehouse stock. According to the standard preliminary factoring strategy for a trinomial with a leading coefficient of 1, which specific conditions must two numbers meet to successfully factor this expression?
An inventory specialist is using the polynomial to model fluctuations in warehouse stock levels. According to the standard preliminary factoring strategy, how is this expression classified to determine the appropriate factoring method?