UNIT FIVE: Lesson 8 – Factoring Polynomial Expressions
1.
COMMON FACTORING

The greatest common factor (GCF) is factored out from ALL expressions before you do anything
else.

The GCF is the biggest number that will divide into all the terms, and for any given variable
(letter), it is the variable with the smallest exponent.
Example: 6 x 3 y 4  9 x 2 y 5  27 x 5 y 4
The GCF is ______________
So, the factored form of this expression is:
2.
FACTORING BY GROUPING

This method is used when you have FOUR OR MORE terms.

It is a “trial & error” method.

Group terms in two’s or three’s and common factor.

If you end up with brackets that are identical, then you have done the factoring correctly. If
not, you must try another “grouping.”
Example: bx  3x  by  3 y
One way to group would be
bx  3x
 by  3 y (i.e., just as written)
The common factor for the first two terms is x . The common factor for the next two terms is
y.
xb  3  yb  3
Note that what remains in the brackets is the same, so you may proceed.
The answer is b  3x  y . And the order of the brackets doesn’t matter.
Example: Factor mx  my  nx  ny
3.
2
FACTORING TRINOMIALS of the form ax  bx  c BY THE “CRISS-CROSS” METHOD.
Example: Factor the following.
a)
x2  2x  1
3
2
d) 2 x  5 x  12 x
2
b) 2 x  5 x  3
2
c) 6 x  5 x  1