- The Factorization Process

Inside Collection (Textbook): Elementary Algebra

Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Factoring is an essential skill for success in algebra and higher level mathematics courses. Therefore, we have taken great care in developing the student's understanding of the factorization process. The technique is consistently illustrated by displaying an empty set of parentheses and describing the thought process used to discover the terms that are to be placed inside the parentheses. The factoring scheme for special products is presented with both verbal and symbolic descriptions, since not all students can interpret symbolic descriptions alone. Two techniques, the standard "trial and error" method, and the "collect and discard" method (a method similar to the "ac" method), are presented for factoring trinomials with leading coefficients different from 1. Objectives of this module: be able to factor a monomial from a polynomial.

- The Factorization Process

We introduce the process of factoring a monomial from a polynomial by examining a problem: Suppose that

Since the product

Now we see that this problem is simply an extension of finding the factors of a monomial.

Thus,

Usually, these divisions can be done mentally and the terms of the factor filled in directly.

The product is

We have the problem:

Since there are four terms in the product, there must be four terms inside the parentheses. To find each of the four terms, we’ll divide (mentally) each term of the product by

Therefore, the other factor is

This result can be checked by applying the distributive property.

Thus,

Again, if the divisions can be performed mentally, the process can proceed very quickly.

The product is

Since there are three terms in the product, there must be three terms inside the parentheses. To find each of these three terms, we’ll divide each term of the product by

The other factor is

The product is

Since there are three terms in the product, there must be three terms inside the parentheses. We will divide (mentally) each term of the product by

The other factor is

Without writing the

The product is

Mentally dividing each term of the original trinomial by

The product is

The product is

The product is

The product is

The product is

For the following problems, the first quantity represents the product and the second quantity a factor. Find the other factor.

*((Reference))* How many

*((Reference))* Find the product.

*((Reference))* Solve

*((Reference))* Given that

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Comments:"Reviewer's Comments: 'I recommend this book for courses in elementary algebra. The chapters are fairly clear and comprehensible, making them quite readable. The authors do a particularly nice job […]"