Diamond and box factoring student version

diamod & box factoring

1. X-box
Factoring

2. X- Box
3 -9
Product
Sum

3. Factor the x-box way
Middle
b=m+n
Sum
Product
ac=mn
m
n
First and
Last
Coefficients
y = ax
2
+ bx + c
Last
term
1st
Term

Factor
n
Factor
m
Base 1 Base 2
GCF
Height

4. Examples
Factor using the x-box method.
1. x
2
+ 4x – 12
a) b) x
-12
4
6 -2
x
2
6x
-2x -12
x
-2
+6
Solution: x
2
+ 4x – 12 = (x + 6)(x - 2)

5. Examples continued
2. x
2
- 9x + 20
a) b)
20
-9
x
2
-4x
-5x 20
x
x-4
-5
Solution: x
2
- 9x + 20 = (x - 4)(x - 5)

-4 -5

6. Examples continued
3. 2x
2
- 5x - 7
a) b)
-14
-5
2x
2
-7x
2x -7
x
2x -7
+1
Solution: 2x
2
- 5x – 7 = (2x - 7)(x + 1)

-7 2

7. Examples continued
3. 15x
2
+ 7x - 2
a) b)
-30
7
15x
2
10x
-3x -2
5x
3x +2
-1
Solution: 15x
2
+ 7x – 2 = (3x + 2)(5x - 1)
10 -3