- Products of Polynomials
- Factoring

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 reminded of products of polynomials, be able to determine a second factor of a polynomial given a first factor.

- Products of Polynomials
- Factoring

Previously, we studied multiplication of polynomials (Section (Reference)). We were given *factors* and asked to find their *product*, as shown below.

Given the factors 4and 8, find the product.

Given the factors

The product is

Given the factors

The product is

Given the factors

The product is

Now, let’s reverse the situation. We will be given the product, and we will try to find the factors. This process, which is the reverse of multiplication, is called *factoring*.

Factoring is the process of determining the factors of a given product.

The number 24 is the product, and one factor is 6. What is the other factor?

We’re looking for a number

To find the number *divide* 24 by 6.

The other factor is 4.

The product is

We know that since

Thus, the other factor is

Checking will convince us that

We should try to find the quotient mentally and avoid actually writing the division problem.

The product is

Mentally dividing

Thus, the other factor is

The product is 84 and one factor is 6. What is the other factor?

14

The product is

In the following problems, the first quantity represents the product and the second quantity represents a factor of that product. Find the other factor.

5

3

1

*((Reference))* Simplify

*((Reference))* Simplify

*((Reference))* Find the product.

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