Factoring Trinomials
Factoring a Trinomial of the Form ax^{2}+ bx+ c
To factor a trinomial of the form ax^{2} + bx
+ c, we can use the grouping method.
Procedure â€”
To Factor ax^{2}+ bx+ c Using the Grouping Method
Step 1 Factor out common factors (other than 1 or 1).
Step 2 Identify the values of a, b, and c.
Then find two integers whose product is ac and whose sum
is b. If no two such integers exist, then the trinomial does
not factor using integers.
Step 3 Replace the middle term, bx, with a sum or difference using
the two integers found in Step 2.
Step 4 Factor by grouping.
Note:
Here is an example of a trinomial that
does not factor using integers:
2x^{2} + x + 3
Here, a = 2, b = 1, and c
= 3.
So, ac = 2
Â· 3 = 6.
Thus, we need to find two integers whose
product ac = 6 and whose sum b = 1.
Here are the possible integer
factorizations for 6:
Factors
1 Â· 6
2 Â· 3
1
Â· 6
2
Â· 3 
Sum
7
5
7
5 
Since none of the sums is the
required 1, we know that 2x^{2} + x + 3 does not factor using integers.
