Factoring Trinomials
Jackie M. Robertson
In the box listed below, the section labeled “Problem” shows the possible signs found in
the trinomials you will factor.
For example, problem one,
y
2
9
y
18
has
(+)
(+)
meaning the first sign in the problem is positive and the second sign is positive.
In
problem three,
y
2
3
y
40
has (+)
( - ) meaning the first sign in the problem is positive
and second sign is negative.
The second column, labeled Factored Signs, tells you what the signs of the factored
problem will be.
In problem one, both signs are positive
y
3
y
6
.
In problem three,
one sign is positive and one sign is negative.
The third column identifies if you should add or subtract the factors of the end term
(c)
for
x
2
bx
c
trinomials to obtain the middle term (bx) of the problem.
For example,
problem one has an end term of 18; the factors of 18 are listed below.
Since the signs in
the factor form of the problem are both positive, you will add the two factors of 18 that
will give you the value 9 in the middle term of the original problem.
How do you know if you have all of the factors of the end term?
You start by dividing
the end term by 1, then 2, then 3, then 4 and so on, looking for the numbers that will
divide the end term evenly.
When you start repeating the factors, such as
3
6
and then
6
3
as in problem one, you have found all of the factors of the end term.
If you do not find two factors, when added or subtracted, that give you the numerical
value of the middle term, then the problem is
prime
and cannot be factored.
Now lets look at each of the problems listed below individually.
We will discuss the
difference of the two types of trinomials
x
2
bx
c
and
ax
2
bx
c
,
a
1
.
Problem
Factored Signs
(+)
(+)
Both positive
Add factor
(+)
( - )
One of each
Subtract factor
( - )
(+)
Both negative
Add factor
( - )
( - )
One of each
Subtract factor
1.

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