Question

Find the greatest common factor. $$9 x, 15 x^{2}$$

   Find the greatest common factor.
$$9 x, 15 x^{2}$$

Prealgebra

Lynn Marecek,… 1st Edition

Chapter 10, Problem 431

Instant Answer

Solved by Expert Debra Garey

04/11/2020

Step 1

The prime factorization of 9 is $3 \times 3$ and the prime factorization of 15 is $3 \times 5$. Show more…

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Find the greatest common factor. $$9 x, 15 x^{2}$$

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Key Concepts

Distributive Property

The distributive property, which states that a·(b + c) equals a·b + a·c, underpins the method of factoring. It allows us to factor out the GCF from an expression, rewriting the original expression as a product of the common factor and a simplified expression.

Variables in Algebraic Expressions

When finding the GCF in algebraic contexts, variables are analyzed by selecting the lowest exponent for each variable that appears in all terms. This approach ensures that the factored variable expression is common to every term.

Greatest Common Factor (GCF)

The greatest common factor is the largest expression that can divide two or more terms without a remainder. It is an important concept in algebra that simplifies expressions and equations by allowing the extraction of common factors from terms.

Prime Factorization

Prime factorization is the process of breaking down integers into their prime number components. This technique is essential for identifying the common numerical factors between terms, which is a critical step in determining the GCF in algebraic expressions.

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