In Exercises 69–78, factor each polynomial.ab − c − ac + b

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Key Concepts

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process is essential for simplifying expressions and solving equations. Common methods include factoring out the greatest common factor (GCF), using special products like the difference of squares, and applying grouping techniques.

Grouping Method

The grouping method is a technique used to factor polynomials with four or more terms. It involves rearranging the terms into groups, factoring out the GCF from each group, and then factoring out the common binomial factor. This method is particularly useful when the polynomial does not easily lend itself to other factoring techniques.

Greatest Common Factor (GCF)

The greatest common factor (GCF) is the largest factor that divides two or more numbers or terms without leaving a remainder. Identifying the GCF is a crucial first step in factoring polynomials, as it simplifies the expression and makes it easier to factor further. In the context of polynomials, the GCF can be a single term or a polynomial itself.