Rules
of Factoring
I. Greatest
Common Factor:
Always factor out
the greatest common factor first.
In other words, find the largest
expression
that divides evenly into all of the terms.
II. 4
- Terms(or more): Factor
by Grouping
If there is no GCF for all of the
terms, but you have 4 or more terms, then
group
together terms that do share common factors.
For example: 
does not have common
factors for
all of the terms. However if we group the first two and last
two terms,
they do have common factors.
Note:
the secret to these is the fact that you will
always get the
same quantities in the parentheses
if you have
factored correctly or if the problem can
be factored by
using the grouping technique.
III. 3
- Terms: Trinomials
To factor trinomials, you begin by
multiplying two binomials. (
)( )
In
order to factor using the techniques of trinomials, the trinomial must be
in one of the following formats:
1. 
2. 
3. 
IV. 2
- Terms : 1. Difference of Squares: 
2. Difference of Cubes: 
3. Sum of Cubes: 
Note: The
Sum of Squares 
cannot be factored using real numbers. We call this
prime for the set of real numbers.