Question

Factor out the GCF. $$ 21 x(x+3)+7 x^{2}(x+3) $$

   Factor out the GCF.
$$
21 x(x+3)+7 x^{2}(x+3)
$$

Prealgebra & Introductory Algebra

Prealgebra & Introductory Algebra

Julie Miller, Molly… 2nd Edition

Chapter 13, Problem 51

Instant Answer

Solved by Expert Matthew Biollo

03/29/2021

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The GCF of 21x and 7x^2 is 7x. Show more…

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Factor out the GCF. $$ 21 x(x+3)+7 x^{2}(x+3) $$

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Key Concepts

Greatest Common Factor (GCF)

The GCF is the largest expression that divides each term of an algebraic expression without leaving a remainder. Recognizing the GCF in a polynomial is essential, as it allows you to simplify the expression by factoring it out, which often makes further manipulation or solving easier.

Distributive Property

The distributive property states that multiplying a sum by a factor is equivalent to multiplying each addend individually by the factor and then adding the products. In factoring, this property is applied in reverse: you take a common factor from each term, which simplifies the expression by grouping like parts together.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of simpler expressions or factors. This technique is fundamental in algebra as it aids in solving equations, simplifying expressions, and understanding the structure of mathematical expressions. Identifying common factors, such as numerical coefficients or binomials, is a key step in the process.

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