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Factoring
Day 1
I can factor a quadratic expression.
2
x + 3x + 2 Rewrite as (x + 1)(x + 2)
3
4
7
21
28
2
6
8
What is the greatest
common factor?
5
6
7
9
35
45
42
54
Example
2
x + 9x + 18
2
ax + bx + c
Multiply a and c
Factors of ac that add to b
ax2
Factor of
ac that
adds to b
x
c
x
Greatest Common Factor
Factor of
ac that
adds to b
x
x
+6
x2
6x
3x
+3
18
Greatest Common Factor
Find 2 numbers that:
Multiply to ac 18
Add up to b: 9
Factors:
Greatest Common Factor
Greatest Common Factor
Factoring Notes
6
3
(x + 6)(x + 3)
a= 1
b= 9
c= 18
x
+4
x2
4x
3x
+3
Greatest Common Factor
x
Example
2
x + 13x + 12
12
Greatest Common Factor
Find 2 numbers that:
Multiply ac
12
Add up to b: 7
Factors:
3
4
(x + 4)(x + 3)
a=
b=
c=
x
x
+ 12
x2
12x
1x
+1
12
Greatest Common Factor
Example
2
x + 7x + 12
Greatest Common Factor
1
7
12
Find 2 numbers that:
Multiply ac
12
Add up to b: 13
Factors:
1
12
(x + 12)(x + 1)
a= 1
b= 13
c= 12
2
x – 8x + 15
x
-5
x2
-5x
-3
-3x
15
Greatest Common Factor
x
List the factors of 15
Greatest Common Factor
x (mult ac): 15
+ (add to b) :-8
-3
-5
Factored form:
a= 1
b= -8
c= 15
(x – 5)(x – 3)
1, 15
3, 5
Multiplying to a positive
Adding to a negative
Sign choices:
+
+
-
-
+
-
-
+
2
x – 8x + 15
x
-5
x2
-5x
-3
-3x
15
Greatest Common Factor
x
List the factors of 15
Greatest Common Factor
x (mult ac): 15
+ (add to b) :-8
-3
-5
Factored form:
a= 1
b= -8
c= 15
(x – 5)(x – 3)
1, 15
3, 5
Multiplying to a positive
Adding to a negative
Sign choices:
+
+
-
-
+
-
-
+
2
x – 2x – 15
x
-5
+3
x2
3x
-5x
-15
Greatest Common Factor
x
List the factors of 15
Greatest Common Factor
x (mult ac): -15
+ (add to b) :-2
3
-5
Factored form:
a= 1
b= -2
c= -15
(x – 5)(x + 3)
1, 15
3, 5
Multiplying to a negative
Adding to a negative
Sign choices:
+
+
-
-
+
-
-
+
I can factor a quadratic expression.
2
x + 3x + 2 Rewrite as (x + 1)(x + 2)
Assignment:
WS 8.5 day 1