Factoring Quadratics
using X-Box
method and Factor by
Grouping
Bell Ringer:
Homework!
• Score out of 26
• Divide by 2.6
X- Marks the Spot
Product
a∙c
factors
factors
Sum
b
Solve using factoring by
grouping
Example: Factor 3x2 -13x -10
1. Plug and solve values of our “X”
3. Solve by grouping! 
-30
2
-13
2. Substitute new factors in for bx
3x2 -15x+2x -10
(3)(-10)=
-15
-13x= -15x+2x
(3x2-15x)+(2x-10)
=3x(x-5)+2(x-5)
=(x-5)(3x+2)
4. Check answer:
3x2 -13x -10=(x-5)(3x+2)
(x-5)(3x+2)
Solve the x-box way
Example: Factor 3x2 -13x -10
x
-5
3x
3x2
-15x
+2
2x
-10
(3)(-10)=
-30
2
-15
-13
3x2 -13x -10
(x-5)(3x+2)
FACTOR the x-box way
ax2 + bx + c
First and
Last
Coefficients
Product
GCF
GCF
ac=mn
GCF
1st
Term
Factor
n
GCF
Factor
m
Last
term
n
m
b=m+n
Sum
Middle
Examples
Factor using the x-box method.
1. x2 + 4x – 12
6
-12
4
-2
x
+6
x
x2
6x
-2
-2x
-12
Solution: x2 + 4x – 12
(x + 6)(x - 2)
Examples
2. x2 - 9x + 20
=(x2-4x)+(-5x+20)
20
-4
-5
-9
x2-4x-5x+20
=x(x-4)-5(x-4)
=(x-4)(x-5)
Solution: x2 - 9x + 20
(x - 4)(x - 5)
Examples
3. 2x2 - 5x – 7
-14
-7
2
-5
2x
x
+1
2x²
2x
Solution: 2x2 - 5x – 7
(2x - 7)(x + 1)
-7
-7x
-7
Examples
4. 15x2 + 7x – 2
3x
-30
10 -3
5x
7
-1
+2
15x²
10x
-3x
-2
Solution: 15x2 + 7x – 2
(3x + 2)(5x - 1)
You Try
• 2x2 +3x –9
• 6x2 + x – 2
• 4x2 + 9x + 2
Partner Activity!
• On the front side of your Factoring Practice are your
questions. On the back side is the answer key for your
partner.
• Work on your own Factoring Practice worksheet and
when you want to check your answer, do so with your
partner.
• Remember the purpose of this activity is to help each
other to be able to solve the problems. Be good
teachers! (Do not just give them the answers)
• Work on for the time given and get as far as you can!