Factoring trinomials in the form
Method 1: Grouping
Find the factors d and e of the product
ac that add to b.Re-write as 
.
Group the first two terms as 
and factor the first group 
by finding the common factor. Now follow the example:
Factor
. Examine factors of the product
and group to get
. Find the common factor to get 
and re-write as
. Making the assumption that this method will work will require the same common factor, so we write 
and we complete this step by inserting
, so
. We see the new common factor 
and we move it out to get the final factored result
.
Method 2: "The BOX"
Begin as in Method 1 (Grouping) by finding the factors d and e of the product
ac that add to b.Make a box as
and fill in
a and c outside along the bottom and d and e on the right outside: 
Then fill in the upper left box with the greatest common positive factor of
a and dExample from above:
Factor. Again we find 2 and -21 and we start the box as:
then insert the greatest common positive factor
and complete the chart with the appropriate multipliers:
Then, find the ultimate factors as follows:
for