Factoring is perhaps the most important skill you will need for much of Beginning Algebra, Intermediate Algebra, and even College Algebra and Finite Math. Let's look briefly at what it means to factor.The Meaning of "to factor."
"To factor" means, "to rewrite as a product (things being multiplied)." For instance, if we were to rewrite 12 as 9 + 3, we would be rewriting it as a SUM (things being added, or as terms). However, if we choose to rewrite 12 as 3 * 4, we would be rewriting it as a PRODUCT (things being multiplied).
Then, we could make the following observations:
- We factored the 12 as 3 * 4.
- And, 3 and 4 are factors of 12.
There are a number of reasons why we factor but perhaps the two most important are:- We factor in order to simplify or reduce algebraic expressions so they are simpler and easier to work with.
- We also factor in order that we may rewrite an equation so it fits the ZEROFACTOR PROPERTY. The Zero- Factor Property, very simply put, says that if the product of two "things" is zero, then one or both of the "things" must be zero. This allows us to set each of the "things" equal to zero and to solve equations we were not able to previously solve.
As a warning, if you don't master it quickly, you will fall behind in understanding and applying new skills and concepts since so many of them will involve factoring. I suggest the following approach:
