Factoring Quadratics with a box

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X-box Factoring
X- Box
Trinomial (Quadratic Equation)
ax2
+ bx + c
Fill the 2 empty sides
with 2 numbers that are
factors of ‘a·c’ and add to
give you ‘b’.
Product of
a & c
b
X- Box
Trinomial (Quadratic Equation)
x2 + 9x + 20
Fill the 2 empty sides
with 2 numbers that are
factors of ‘a·c’ and add to
give you ‘b’.
20
5
4
9
X- Box
Trinomial (Quadratic Equation)
2x2 -x - 21
Fill the 2 empty sides
with 2 numbers that are
factors of ‘a·c’ and add to
give you ‘b’.
-42
-7
6
-1
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
LET’S TRY IT!
Students apply basic factoring techniques to secondand simple third-degree polynomials. These
techniques include finding a common factor for all
terms in a polynomial, recognizing the difference of
two squares, and recognizing perfect squares of
binomials.
Objective: I can use the x-box method to factor
non-prime trinomials.
Factor the x-box way
Example: Factor x2 -3x -10
(1)(-10)=
x
-10
-5
-5
x
x2
-5x
GCF
+2
2x
-10
GCF
GCF
GCF
2
-3
x2 -3x -10 = (x-5)(x+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
Factor the x-box way
Example: Factor 3x2 -13x -10
x
-5
3x
3x2
-15x
+2
2x
-10
-30
2
-15
-13
3x2 -13x -10 = (x-5)(3x+2)
Examples
Factor using the x-box method.
1. x2 + 4x – 12
a)
x
b)
6
-12
4
-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
x2
-4
-4x
-5 -5x 20
Solution: x2 - 9x + 20 = (x - 4)(x - 5)
Examples continued
3. 2x2 - 5x - 7
a)
b)
-14
-7
-5
2x
2
x
+1
-7
2x2 -7x
2x -7
Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)
Examples continued
3. 15x2 + 7x - 2
a)
-30
10
-3
7
b)
3x
+2
5x 15x2 10x
-1
-3x
-2
Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)
Extra Practice
1. x2 +4x -32
2. 4x2 +4x -3
3. 3x2 + 11x – 20
Reminder!!
Don’t forget to check your
answer by multiplying!

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