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Factoring 26rs, 52r, 39rs: Solution

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factor 26r3s 52r5 39r2s4 what is the resulting expression

Factoring 26rs, 52r, 39rs: Solution

The process involves finding the greatest common factor (GCF) of the terms 26rs, 52r, and 39rs. The GCF is the largest expression that divides evenly into all given terms. In this case, the coefficients 26, 52, and 39 share a common factor of 13. The variables r and s also appear in each term. The lowest power of r present is r, and the lowest power of s is s. Therefore, the GCF is 13rs. Dividing each term by the GCF yields the factored expression: 13rs(2rs + 4r + 3s).

Factoring expressions plays a crucial role in simplifying algebraic equations and expressions. This simplification allows for easier manipulation and solution of complex mathematical problems. Historically, the development of factoring techniques contributed significantly to advancements in algebra and number theory. It allows mathematicians to break down complex expressions into simpler components, revealing underlying structures and relationships.

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Factoring 15x-5x+6x-2 by Grouping: Solution

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factor 15x3-5x2+6x-2 by grouping. what is the resulting expression

Factoring 15x-5x+6x-2 by Grouping: Solution

Factoring by grouping is a technique used to factor polynomials with four or more terms. In the given example, 15 x3 – 5x2 + 6x – 2, the terms are grouped into pairs: (15 x3 – 5x2) and (6x – 2). The greatest common factor (GCF) is then extracted from each pair. The GCF of the first pair is 5 x2, resulting in 5x2(3x – 1). The GCF of the second pair is 2, resulting in 2(3x – 1). Since both resulting expressions share a common binomial factor, (3x – 1), it can be further factored out, yielding the final factored form: (3x – 1)(5*x2 + 2).

This method simplifies complex polynomial expressions into more manageable forms. This simplification is crucial in various mathematical operations, including solving equations, finding roots, and simplifying rational expressions. Factoring reveals the underlying structure of a polynomial, providing insights into its behavior and properties. Historically, factoring techniques have been essential tools in algebra, contributing to advancements in numerous fields, including physics, engineering, and computer science.

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9+ Tips: What is Written Expression & Why It Matters

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what is written expression

9+ Tips: What is Written Expression & Why It Matters

Communication conveyed through the medium of text, crafted with purpose and intentionality, represents a fundamental skill. It encompasses the ability to articulate thoughts, ideas, and information coherently and effectively through written language. For example, a well-structured report, a compelling narrative, or a clear set of instructions all demonstrate this competency.

The power to communicate effectively in this manner provides numerous advantages. It enables the precise and permanent record of information, facilitating collaboration, knowledge transfer, and institutional memory. Historically, it has served as a cornerstone of education, commerce, and governance, allowing societies to organize, preserve knowledge, and advance through sustained and reasoned discourse. Its mastery unlocks opportunities in diverse fields, from journalism and academia to business and technology.

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