In Exercises 35–44, factor the greatest common binomial factor from each polynomial.(x + 2)(x + 3) + (x − 1)(x + 3)

Factoring polynomials involves breaking down a polynomial into simpler components, or factors, that when multiplied together yield the original polynomial. This process is essential for simplifying expressions and solving equations. In this case, recognizing common factors in the given polynomial expression is crucial for effective factoring.

The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers or expressions without leaving a remainder. In polynomial expressions, identifying the GCF allows for the simplification of the expression by factoring it out, making it easier to work with. This concept is key to solving the problem presented.

A binomial expression is a polynomial that consists of two terms, typically connected by a plus or minus sign. In the context of the given problem, recognizing the binomial factors within the polynomial is essential for factoring out the GCF. Understanding how to manipulate and factor binomials is a fundamental skill in algebra.