Factoring
Quadratics
Special Factoring
Patterns
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Difference of Squares
a2 – b2 = (a + b)(a – b)
Example:
x2 – 36 = (x + 6)(x – 6)
a2 – 49 = (x + 7)(x – 7)
Special Factoring
Patterns
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Perfect Square Trinomial
a2 + 2ab + b2 = (a + b)2
a2 - 2ab + b2 = (a - b)2
Example:
a2 + 8a + 16 = (a + 4)2
a2 – 10a + 25 = (a - 5)2
X-box
Factoring
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
Standard 11.0
Students apply basic factoring techniques to
second- and 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
y = ax2 + bx + c
First and
Last
Coefficients
Product
GCF
GCF
ac=mn
1st
Term
Factor
n
Factor
m
Last
term
n
m
b=m+n
Sum
Middle
GCF
GCF
Examples
Factor using the x-box method.
1. x2 + 4x – 12
a)
6
-12
4
x
b)
-2
x
-2
x2
+6
6x
-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)
Guided Practice
Grab your worksheets,
pens and erasers!
Practice
Factor:
2
x – 7x +10
(x -5)(x – 2)
q2 – 11q +28
(q - 7)(q – 4)
Practice
Factor:
2
x – 81
(x - 9)(x + 9)
q2 – 26q +169
(q - 13)2
Practice
Factor:
2
x – 49
(x - 7)(x + 7)
q2 – 16q + 64
(q - 8)2