In Exercises 45–68, factor by grouping. 4x³ − x² + 12x - 3

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 looking for a 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 effectively.

Polynomial terms are the individual components of a polynomial expression, consisting of coefficients and variables raised to non-negative integer powers. Understanding the structure of polynomial terms is essential for factoring, as it helps in identifying how to group and manipulate the terms to achieve a simpler form.