ax 2
 bx c
a

1
1. Construct product/sum chart and determine the pair of numbers
(factor pair) which has a product equal to the value of c
and a sum equal to the value of b
.
For example, if factoring x
2 
4 x a product of -12 and a sum of 4.

12
, find the factor pair which yields
PRODUCT = - 12
1
 
12
SUM = 4
1 ( 12)
 
11 Not Good
1 12
2
 
6
1 12 11 Not Good
2 ( 6) 4 Not Good
2 6 2 6 4 WORKS!
2. Insert the factor pair directly into the constant locations in the binomial factors. Since the factor pairs turned out to be -2 and 6, the factored form is  x

2
 x

6

.
Check your answer by multiplying.

ax 2  bx c
a

0,1
1. Construct product/sum chart in same manner as for trinomials where a=1 HOWEVER, determine the factor pair which has a product equal to the value of a c
and a sum equal to the value of b
.
For example, given the trinomial
6 x
2 
17 x

14
, you would look for a factor pair which has a product of -84 (from
6
 
14
) and a sum of -
17. In this case, the factor pair turns out to be 4 and -21.
2. Use this factor pair to break the linear (middle) term into two parts:
6 x
2 
17 x

14 becomes
6 x
2 
21 x

4 x

14
3. Group the first two terms and the last two terms and factor out the
GCF from each of the groups:
(6 x
2  x
 x

14)
3 (2 x
  x

7)
4. Complete by factoring out the GCF between groups. In this case, the GCF is the binomial (2x-7).

2 x
  x

2

.
5. Check your answer by completing the multiplication.