1
Lessons 27
Factoring Trinomials, Perfect Square Trinomials, Difference of Squares
TRINOMIALS (leading coefficient not a 1)
Form:
cbxax ++
2
Always write terms in descending order!
Notice: 156151096)32)(53(
22
−−=−−+=+− xxxxxxx
2
6
x
is the product of the first two terms, -15 is the product of the last two terms,
-
x
is the sum of the outer and inner terms
There are two methods that can be used to factor trinomials
of the form
,
2
.
ax bx c
+ +
The first method is a ‘trial-and-error’ process or ‘reversing FOIL’.
The second method is called the ‘Grouping Method’ or Product/Sum Method. I will
show both methods and you may choose which method works for you. I recommend
the Grouping Method.
Trial-and-Error Method:
1.
Make your first terms have a product of
2
ax
.
2.
Make your last terms have a product of
c
.
3.
Find the sum of the inner and outer terms and check if it equals
bx
. If not, go
back to steps 1 and 2 and try a different combination, until step 3 checks.
OR
Grouping Method (Product/Sum Method)
Follow these steps:
1.
If the trinomial is in the form
cbxax ++
2
, find a pair of numbers whose product
is
ac
and whose sum is
b
. Call these numbers
r
and
s
.
2.
Write the polynomial of the form
csxrxax +++
2
. Use the ‘grouping’ method to
factor. (This method will be demonstrated in class.)
Factor:
1) 2556
2
−− xx
2) 8189
2
++ aa
