Factor each polynomial by grouping. See Example 2. 10ab-6b+35a-21

Factoring by grouping is a method used to factor polynomials that have 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 common factor across all terms.

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 the given polynomial, recognizing the common factors in pairs of terms is essential for successful grouping and factoring.

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, after extracting common factors from grouped terms, the resulting expression often reveals a binomial factor. Understanding how to identify and manipulate binomial factors is key to simplifying and solving polynomial equations.