Factoring when a=1 and c > 0.
x

2
 8x  12
First list all the factor pairs of c. 1 , 12 -1, -12
2,6
3,4

Then find the factors with a sum of

These numbers are used to make the
factored expression.
x
 2x  6
-2, -6
-3, -4
b
Now you try.
x
2
 8x  15
x
Factors of c:
2
 10x  21
Factors of c:

Circle the factors of c with
the sum of b
Circle the factors of c with
the sum of b
Binomial Factors
(
)(
Binomial Factors
)
(
)(
)
Factoring when c >0 and b < 0.

c is positive and b is negative.
 Since a negative number times a negative
number produces a positive answer, we can
use the same method as before but…
 The binomial factors will have subtraction
instead of addition.
Let’s look at
x  13x  12
2
First list the factors of 12
1
We need 
a sum of -13 2
12
-1, -12
6
-2, -6
3 4 -3, -4
Make sure both values are negative!
x
 12x  1
Now you try.
2
1. x  7x  12
2. x  9x  14
2
3. x 13x  42
2
Factoring when c < 0.
We still look for the factors of c.
However, in this case, one factor should be
positive and the other negative in order to get a
negative value for c
Remember that the only way we can
multiply two numbers and come up
with a negative answer, is if one is
number is positive and the other is
negative!
Let’s look at
x  x  12
2
In this case, one factor -1, 12
should be positive and
-2, 6
the other negative.

We need a sum of -1
x
 3x  4
-3, 4
1, -12
2, -6
3, -4
Another Example x  3x  18
2
List the factors of 18.
We need a sum of 3

What factors and signs
will we use?
x
 3x  6
1
18
2
9
3
6

Now you try.
1.
2.
3.
4.
x
2
 3x  4
x
2
 x  20
x
2
 4 x  21
x
2
 10x  56
Prime Trinomials
Sometimes you will find a quadratic
trinomial that is not factorable.
You will know this when you
cannot get b from the list of
factors.
When you encounter this
write not factorable or
prime.
Here is an example…
x  3x  18
2
1
18
2
9
3
6
Since none of the pairs adds to 3,
this trinomial is prime.
Now you try.
x
2
 6x  4
x
2
 10x  39
x
2
 5x  7
factorable
factorable
factorable
prime
prime
prime