In Exercises 45–68, factor by grouping. x² + 7x − 4x − 28

Factoring by grouping is a method used to factor polynomials with four or more terms. This technique involves rearranging the terms into two groups, factoring out the common factors from each group, and then factoring out the common binomial factor. It is particularly useful when the polynomial does not have a straightforward factorization.

A common factor is a number or variable that divides two or more terms without leaving a remainder. Identifying common factors is crucial in factoring polynomials, as it allows for simplification of expressions. In the context of grouping, recognizing the common factors in each group helps in extracting them to facilitate further factorization.

A binomial factor is a polynomial that consists of two terms, typically expressed in the form (ax + b). In the process of factoring by grouping, the goal is often to identify and factor out a common binomial from the grouped terms. Understanding how to manipulate and factor binomials is essential for successfully applying this method.