Chapter 6 - Factoring

Following an overview of the prime factorization of integers and the concept of a greatest common factor, this chapter moves on to discuss how to find and factor out the greatest common factor for monomials. There is then a discussion of how to factor special products such as a difference of two squares, and a perfect square trinomial. The concept of factoring completely to prime polynomials is explained, followed by a discussion of factoring by grouping. This is followed by a discussion of factoring trinomials of the form ax² + bx + c with a = 1, looking also at situations in which this expression is a prime polynomial. Factoring with two variables is then considered, as well as the complete factoring of polynomials of degree three. Next, the factoring of trinomials of the form ax² + bx + c with a not equal to 1 is discussed. The ac method is introduced, and again examples are given of complete factoring of third-degree polynomials. Then there is a look at how division relates to factoring, with an investigation of two special cases, namely factoring the difference and sum of two cubes. All the ideas of the chapter are brought together and summarized as a general factoring strategy. The chapter then concludes with a discussion of solving quadratic equations by factoring, making use of the Zero Factor Property. Several examples are presented, including an equation with three solutions.

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