X-box
Factoring
X- Box
Product
3
-9
Sum
X-box Factoring
• This is a guaranteed method for
factoring quadratic equations—no
guessing necessary!
• We will learn how to factor quadratic
equations using the x-box method
• Background knowledge needed:
– Basic x-solve problems
– General form of a quadratic equation
– Dividing a polynomial by a monomial using the
box method
Factor the x-box way
Example: Factor 3x2 -13x -10
(3)(-10)=
-30
2
-15
x
-5
3x
3x2
-15x
+2
2x
-10
-13
3x2 -13x -10 = (x-5)(3x+2)
Factor the x-box way
y = ax2 + bx + c
First and
Last
Coefficients
Product
Base 1
Base 2
ac=mn
GCF
1st
Term
Factor
n
Height
Factor
m
Last
term
n
m
b=m+n
Sum
Middle
Examples
Factor using the x-box method.
1. x2 + 4x – 12
a)
6
-12
4
x
b)
-2
+6
x
x2 6x
-2
-2x -12
Solution: x2 + 4x – 12 = (x + 6)(x - 2)
Examples
continued
2. x2 - 9x + 20
a)
20
-4 -5
-9
x
b)
x
-4
x2 -4x
-5 -5x 20
Solution: x2 - 9x + 20 = (x - 4)(x - 5)