Factoring
Factor by identifying and extracting a binomial greatest common factor (GCF).
The expression consists of two terms: and . Both terms share the common binomial factor , which serves as the GCF. Just as a monomial GCF is factored out using the reverse Distributive Property, a binomial GCF is factored out in the exact same way.
Factor the GCF, : Write the binomial GCF outside the parentheses and place the remaining factors — and — inside a second set of parentheses:
Check by multiplying: Distribute back through to verify the result equals the original expression.
The factored form is . This example demonstrates that the GCF of a polynomial does not have to be a monomial — it can be an entire binomial expression. Whenever every term of a polynomial contains the same binomial factor, that binomial can be factored out.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.7 Factoring - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Intermediate Algebra @ OpenStax
Ch.6 Factoring - Intermediate Algebra @ OpenStax
Related
Factoring
Factoring
Factoring
Factoring with a Negative Leading Coefficient
Factoring
Factoring
Factoring by Grouping
Factoring
Factoring
An operations analyst is streamlining a production cost formula to identify shared expenses. To correctly factor the Greatest Common Factor (GCF) from the cost polynomial, in what order should the following steps be performed?
A logistics coordinator is simplifying a shipping cost formula by factoring out the greatest common factor (GCF). Arrange the standard steps for factoring the GCF from a polynomial in the correct order.
A budget analyst is simplifying a departmental expense formula, $15x + 15y, to identify a shared hourly rate. By rewriting the expression as $15(x + y), the analyst is applying which mathematical property in reverse?
A business analyst is simplifying a revenue formula to identify shared cost drivers across different departments. Match each mathematical term or process with its correct role in the procedure of factoring out the Greatest Common Factor (GCF).
A payroll specialist is simplifying a bonus calculation formula: 50h + 50b. After factoring the expression as 50(h + b), the specialist wants to verify the result. According to the standard procedure for factoring the Greatest Common Factor (GCF), the specialist should check the work by distributing the 50 back through the parentheses to ensure the product matches the original formula.
Procedural Steps for Factoring Overhead Costs
Optimizing Assembly Line Output Formulas
A data analyst is simplifying a revenue calculation by identifying the greatest common factor (GCF) shared by all terms. This procedural step is mathematically defined as the reverse of __________ a polynomial by a monomial.
Standard Operating Procedure for Factoring Shared Resource Costs
A production analyst is simplifying a formula to identify shared manufacturing costs across multiple assembly lines. According to the standard procedure for factoring the Greatest Common Factor (GCF) from a polynomial, which method is recommended to identify the largest expression that divides evenly into every term?
Factoring
Factoring
General Strategy for Factoring Polynomials
Learn After
A project manager uses the expression '5q(q + 7) - 6(q + 7)' to model labor costs for two project phases. Which binomial represents the Greatest Common Factor (GCF) shared by both terms in this expression?
A facilities manager uses the expression 5q(q + 7) - 6(q + 7) to represent the total area of two office suites. In this expression, the binomial that represents the common width (the Greatest Common Factor) of both suites is ____.
A production supervisor uses the expression 5q(q + 7) - 6(q + 7) to model the output of two assembly lines. Match each part of the expression to its correct mathematical role in the factoring process.
A manufacturing engineer uses the expression $5q(q + 7) - 6(q + 7)$ to model the stress levels on two different structural components. Arrange the following steps in the correct order to factor this expression by identifying and extracting the binomial Greatest Common Factor (GCF).
Identifying the Remaining Binomial Factor
A facilities manager uses the expression $5q(q + 7) - 6(q + 7)(q + 7)$ serves as the Greatest Common Factor (GCF) that can be extracted using the reverse Distributive Property.
Operational Efficiency Formula Analysis
Standardizing Cost Model Simplification
A logistics coordinator uses the expression $5q(q + 7) - 6(q + 7)$ to represent the total distribution of resources across two shipping zones. Which of the following represents the correctly factored form of this expression?
A corporate technical instructor uses the expression $5q(q + 7) - 6(q + 7)$ to demonstrate factoring techniques to a group of analysts. According to the lesson, what important principle regarding the Greatest Common Factor (GCF) is illustrated by this specific example?