Factoring is a process used to solve algebraic expressions. An essential aspect of factoring is learning how to find the greatest common factor (GCF) of a given algebraic problem. Once the …

1) 1)(x 4) = 3(5x2 21x + 4) as desired. Thus, our factorization is 3(5x 1)(x 4).

As always when factoring, you should first check to see if you can factor out a GCF before trying any other technique. In the last sections, we will put all of our techniques together.

Example: The polynomial 2x + 2 is irreducible over R since any factorization results in at least one unit, for example 2x + 2 = 2(x + 1) doesn't count since 2 is a unit.

The following factorization is easy (for an factorization result, so not so easy overall) because it puts the triangular matrices on the outside. It is great for theory, a bit lame in applications.

Although, as a practical matter, not all polynomials can be factored, the methods described below will work for virtually all polynomials we run across which can be factored. Our method …

We say that a divides c, writing ajc, to mean: There exists b 2 S with a ? b = c. ), does 3j6? 6j3? 3j5? Ex2: (N0; +), does 3j5? 6j3? If there is an identity I, and xjI, we call x a unit. The good …