Factoring
To factor , determine the greatest common factor (GCF) of the three terms. The numerical GCF of , , and is , and the shared variables with the lowest exponents are and . Thus, the GCF is . Factoring out of each term produces the simplified expression: .
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Intermediate Algebra @ OpenStax
Ch.6 Factoring - Intermediate Algebra @ OpenStax
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Factoring
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Factoring with a Negative Leading Coefficient
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Factoring by Grouping
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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
Binomial Greatest Common Factor
Factoring
Factoring
Simplifying a Trinomial by Factoring the GCF to Reveal a Leading Coefficient of 1
Factoring a Negative Greatest Common Factor
Learn After
A warehouse manager uses the algebraic expression to model the distribution of inventory across three storage zones. To simplify the inventory report, the manager must first identify the greatest common factor (GCF) for the terms in this expression. What is the GCF?
An energy auditor is modeling the heat loss from three different building zones using the expression . To simplify the model and calculate a common loss factor, the auditor determines the Greatest Common Factor (GCF) and factors it out. Match each component of this factoring process to its corresponding mathematical result.
A logistics coordinator uses the expression to model fuel consumption across three distinct delivery routes. To simplify the tracking model, the coordinator factors out the Greatest Common Factor (GCF). True or False: The correctly factored form of this expression is .
An environmental scientist uses the expression to calculate the concentration of pollutants in a water system. To simplify the calculation, the scientist factors out the Greatest Common Factor (GCF), which is . Arrange the three resulting terms that remain in the parentheses in order from the highest power of to the lowest.
Identifying the Greatest Common Factor in Logistics Modeling