The document provides instructions and examples for factoring quadratic expressions using the box method. It explains the steps as: 1) Draw a box and write the coefficients of the quadratic term, linear term, and constant term. 2) Find two numbers whose sum is the linear coefficient and whose product is the constant term. 3) Write these two numbers above and below the box to factor the expression. Several examples are worked out step-by-step and the reader is prompted to try additional problems and check their own work.

1. Box Method
Factoring

2. Factor the box method
way
Middle
b=m+n
Sum
Product
ac=mn
m n
First and
Last
Coefficients
y = ax2
+ bx + c
Last
term
1st
Term
Factor
n
Factor
m
Base 1 Base 2
GCF
Height

3. Examples:
Factor using the x-box method.
1. x2
+ 4x – 12
a) b) x
-12
4
6 -2
x2
6x
-2x -12
x
-2
+6
Solution: x2
+ 4x – 12 = (x + 6)(x - 2)

4. You Try:
2. x2
- 9x + 20
a) b)
20
-9

5. 2. x2
- 9x + 20
a) b)
20
-9
x2
-4x
-5x 20
x
x -4
-5
Solution: x2
- 9x + 20 = (x - 4)(x - 5)
-4 -5
Check yourself:

6. Think-Pair-Share
1. Try this problem using the box
method: x2
+4x -32.
2. Trade papers with your partner and
use their steps to factor the
following problem: x2
+4x -32.

7. Examples:
3. 2x2
- 5x - 7
a) b)
-14
-5
2x2
-7x
2x -7
x
2x -7
+1
Solution: 2x2
- 5x – 7 = (2x - 7)(x + 1)
-7 2

8. You Try:
3. 15x2
+ 7x - 2
a) b)
-30
7

9. Check Yourself:
3. 15x2
+ 7x - 2
a) b)
-30
7
15x2
10x
-3x -2
5x
3x +2
-1
Solution: 15x2
+ 7x – 2 = (3x + 2)(5x - 1)
10 -3

10. Check Yourself:
3. 15x2
+ 7x - 2
a) b)
-30
7
15x2
10x
-3x -2
5x
3x +2
-1
Solution: 15x2
+ 7x – 2 = (3x + 2)(5x - 1)
10 -3