Factoring Ax2 + Bx + C using the “AC” Method
Step 1
F
Factor
out any GCF.
G F Find
F d AC of
f the
h “new”
“
” trinomial.
l
Five Steps
p
Copyright 2003 Edwin Ellis
www.GraphicOrganizers.com
If no GCF, find AC of original trinomial.
Step 2
List all factor pairs (positive & negative) of AC.
Find the one p
pair whose sum equals
q
C.
Step 3
Why are
these
steps
important?
Note: The integers in the factor pair found in
the previous step are the outer/inner products,
not necessarily
l the
h numbers in the
h binomials.
l
These steps enable
us to:
•factor any
polynomial not
prime
•determine xintercepts of a
parabola
•use x-intercepts to
graph
Step 4
If A or C is prime, that is where you start when
writing your binomials
binomials. If not
not, look for common
factors between A,C & the factors from Step 2.
Step 5
(
)(
) Make the outer/inner products equal
the factors you found in Step 2. Check by
multiplying everything. (It should equal original problem.)
Factoring Ax2 + Bx + C
Example using the AC Method:
Find AC.
Factor out
GCF.
12x2 + 17x – 7
This problem
has no GCF
GCF.
A = 12 & C = -7
so AC =
12(-7)
12(
7) = 84
See if A or C is
prime. C = 7…
7 & 21
21… makes
one think of 3
(
1)(
7)
Now check 7 with
desired outer/inner
products, -4 & 21.
12x2 + 17x – 7
Find factors of -84
whose sum is 17.
Factors of -84 are
-1 & 84, 84 & -1,
-2 & 42, 2 & -42,
-3
3 & 28, 3 & -28,
28,
-4 & 21, 4 & -21,
-7 & 12, 7 & -12
Hmm…
-4
4 + 21 = 17
These will be the
outer/inner
“FOIL” p
products
of binomials.
Other desired
product is -4.
Check by
multiplying.
(3x 1)( + 7)
(3x – 1)(4x +7)
(3x – 1)(4x + 7)
So put 3 opposite the
7 to get 21 & put plus
in front of 7 so it’s
positive 21.
So put in 4x and
make the 1
negative.
12x2 + 21x – 4x -7
=12x2 + 17x - 7
So what? What is important to understand about this?
Factoring is used in many real world applications such as carpentry, architecture, many types of science fields. Factoring is also
vital to upper level math courses. Work hard to become confident with factoring.