Factor out the greatest common factor from each polynomial. See Example 1. 2(a+b)+4m(a+b)

Verified step by step guidance

1. Identify the common factor in each term of the polynomial. In this case, the common factor is \((a+b)\).
2. Rewrite each term of the polynomial to highlight the common factor: \(2(a+b) + 4m(a+b)\).
3. Factor out the common factor \((a+b)\) from each term.
4. Express the polynomial as a product of the common factor and the remaining terms: \((a+b)(2 + 4m)\).
5. Verify the factorization by distributing \((a+b)\) back into the expression to ensure it equals the original polynomial.

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers or expressions without leaving a remainder. In polynomial expressions, the GCF is the highest degree of common variables and the largest numerical coefficient shared among the terms. Identifying the GCF is crucial for simplifying expressions and factoring polynomials effectively.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors, which can include numbers, variables, or other polynomials. This process simplifies expressions and makes it easier to solve equations. Understanding how to factor polynomials is essential for solving algebraic problems and is a foundational skill in algebra courses.

Distributive Property

The Distributive Property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within a parenthesis. This property is fundamental in both expanding and factoring expressions. When factoring out the GCF, recognizing how to apply the Distributive Property in reverse is key to rewriting the polynomial correctly.