Factoring R5

1
Factoring (R5)
2
F O I L
2x
2 x
25
x2
5x
x 5
3
The Sum The Product of 2 5
2x
25
x2
5x
x2 (25)(x) (25)
4
The Sum The Product of 2 5
(x 2) (x 5)
x2 (25)(x) (25)
product
sum
5
The Sum The Product of a b
(x a) (x b)
x2 (ab)(x) (ab)
product
sum
x2 (B)(x) (C)
6
So What?

• We can use this knowledge
• to factor anything easily.

7
The factors of C add up to B.
B C
x2 7x 10
Example
Factors of 10 1 10 2 5
(x 2) (x 5)
8
The factors of C add up to B.
B C
x2 - 1x - 12
Example
Factors of -12 -1 12 -2 6 -3 4 -4 3
(x 4 ) (x 3)
9
The factors of C add up to B.
B C
x2 12x 35
Example
Factors of 35 1 35 5 7
(x 5 ) (x 7)
10
The factors of C add up to B.
B C
x2 10x - 39
Example
Factors of -39 -1 39 -3 13
(x - 3 ) (x 13)
11
x4 7x2 10
Let v x2
v2 7v 10
12
v2 7v 10
(v 2) (v 5)
v x2, so
(x2 2) (x2 5)
Can either of these be factored?
No? Then, done.
13
But what about things like2x2 5x 3

• (when the leading coefficient
• is not just a one)

14
2x2 5x 3
15
2x2 5x 3
Factors of 3
Factors of 2
1 3
1 3
1
2 6
2
16
3x2 - 14x 8
1 8 2 4
3 24 6 12
17
3x2 - 14x 8
1 8 2 4
2 12 14
3 24 6 12
-2 -12 -14
18
8x2 18x 9
1 9 3 3
8 72 24 24
2 18 6 6
4 36 12 12
19
8x2 18x 9
1 9 3 3
8 72 24 24
2 18 6 6
4 36 12 12
20
Homework

• p. 51
• 5-31, 39-49, 57-95
• p.123 41-49 (factor only)