Question

Factor out the GCF. $$ 7 x 5-21 x 3-14 x_{2}+28 x $$

   Factor out the GCF.
$$
7 x 5-21 x 3-14 x_{2}+28 x
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 6, Problem 47

Instant Answer

Solved by Expert Emily Himsel

01/27/2022

Step 1

The GCF is the largest number or term that can be divided evenly into each term of the expression. In this case, the GCF is $7x$. Show more…

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Factor out the GCF. $$ 7 x 5-21 x 3-14 x_{2}+28 x $$

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Key Concepts

Greatest Common Factor (GCF)

The GCF is the largest expression, including numerical coefficients and variable factors, that divides all terms in a polynomial without leaving a remainder. Identifying the GCF is a critical first step in simplifying expressions and factoring, as it allows one to reduce the polynomial by extracting common factors.

Factoring Polynomials

Factoring polynomials is the process of rewriting a polynomial as a product of simpler expressions, which makes solving equations and simplifying calculations more manageable. Recognizing and extracting common factors is one of the basic techniques used in this process.

Distributive Property

The distributive property underlies the process of factoring by allowing one to factor out a common term from multiple terms in an expression. It states that a(b + c) = ab + ac, and when factoring, this property is applied in reverse to consolidate shared factors.

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