Math 0308/math 0310 Factoring Polynomials Worksheet With Answer Key - Lone Star College Montgomery, 2011 Page 2
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2
3Factoring by Grouping
This method is used when there are four (4) terms in the polynomial.
3xy – 6x + 2y – 4
Example:
= (3xy – 6x) + (2y – 4)
group the terms into pairs
= 3x(y – 2) + 2(y – 2)
take out the GCF from each pair
= (y – 2)( 3x + 2)
take out the common binomial factor
Factoring a Trinomial by the Reverse FOIL Method
Consider multiplying
(
F
L F
)(
L :
)
1
1
2
2
F = First =
F F , O = Outer =
F L , I = Inner =
L F , L = Last =
L L
1
2
1
2
1
2
1
2
Examples
F
O
I
L
Result
=
2x
1x
2
=
(
x
1)(
x
2)
2
2
x
x + 3x + 2
(
x
3)(
x
4)
=
2
4x
-3x
-12
=
2
x
x + x
12
(2
x
1)(
x
5)
=
2
-10x
1x
-5
=
2
x
x
9x 5
(3
x
2)(
x
3)
=
-9x
-2x
6
=
2
2
x
x
11x+ 6
The Reverse FOIL Method is simply transforming the Result column back to the first column.
In other words, factoring a trinomial means writing it as a product of factors.
2
The Result column is in the form of a trinomial,
ax
bx c . Notice that:
the first term equals the value in column F
the middle term equals O + I
the last term equals L
Steps:
1) Factor the first term into the “F” positions: (
F
) (
F
).
1
2
2) Factor the last term into the “L” positions: (
L ) (
L ).
1
2
3) Check the factoring by FOIL. Make sure Outer and Inner add up to the middle term. If not, try switching
factors and signs inside the parentheses until the FOIL result equals the trinomial.
Factoring a Trinomial by the ac-Method
Steps:
1) Find the value of a c
2) Look for factors of ac that will add to b
3) Split the middle term into two terms with the result in step (2)
4) Factor by grouping
2
3
x
10
x
8
Example:
a = 3, b = -10, c = -8
1. (3)(-8) = -24
2. Look for factors of -24 that will add to -10
-24 = 2 -12
2 + (-12) = -10
2
2
3.
3
x
10
x
8
=
3
x
2
x
12
x
8
= x(3x + 2) – 4(3x + 2) = (3x + 2)(x – 4)
2
4.
3
x
2
x
12
x
8
LSC-Montgomery Learning Center: Factoring Polynomials
Page 2
Last Updated April 13, 2011
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