Luttrell 2012
115
Name: ______________________
Date: _____
8b – Factoring
Factoring when
a
= 1,
c
> 0:
A quadratic e
x
pression of
ax
2
±
bx
+
c
where
a
= 1 looks like
x
2
±
bx + c
. This e
x
pression can be
factored into (
x+d
)(
x+ e
) or (
x-d
)(
x-e
) whenever the
c
term divisors sum up to the middle term
b
.
Note how both factors have the same sign as
b
whenever
c
>0.
E
x
ample A:
x
2
+ 5
x
+ 6
Y
ou probabl
y
won’t have more than one line of
( )( )
work on
y
our paper. But these are the steps to fill
(
x
)(
x
)
in the parentheses. Note (
x
2)(
x
3) was chosen
Choices: (
x
1)(
x
6) Or (
x
2)(
x
3) because 2 + 3 = 5. The signs are usuall
y
the last.
Answer: (
x
+ 2)(
x
+ 3)
E
x
ample B:
x
2
- 12
x
+ 36
( )( )
Fill in the missing numbers!
(
x
)(
x
)
Choices: (
x
±
)(
x
3) or (
x
1)(
x
36) or (
x
2)(
x
18) or (
x
4)(
x
±
) or (
x
6)(
x
±
)
Answer: (
x
- 6)(
x
- 6)
Factor. Check work.
1.
x
2
+ 4
x
+ 3
2.
x
2
- 2
x
+ 1
3.
x
2
+ 6
x
+ 8
4.
x
2
+ 7
x
+ 12
5.
x
2
- 14
x
+ 24
6.
x
2
- 11
x
+ 24
7.
x
2
+ 9
x
+ 18
8.
x
2
- 10
x
+ 24
9.
x
2
+ 11
x
+ 18
10.
x
2
+ 9
x
+ 20
11.
x
2
+ 13
x
+ 40
12.
x
2
- 5
x
+ 4
