1. Factoring Quadratics

2. Special Factoring Patterns
Difference of Squares
a2 – b2 = (a + b)(a – b)
Example:
x2 – 36 = (x + 6)(x – 6)
a2 – 49 = (x + 7)(x – 7)

3. Special Factoring Patterns
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

4. X-box Factoring

5. 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

6. 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.

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

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

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

10. Guided Practice
Grab your worksheets, pens and erasers!

11. Practice
Factor:
x2 – 7x +10
(x -5)(x – 2)
q2 – 11q +28
(q - 7)(q – 4)

12. Practice
Factor:
x2 – 81
(x - 9)(x + 9)
q2 – 26q +169
(q - 13)2

13. Practice
Factor:
x2 – 49
(x - 7)(x + 7)
q2 – 16q + 64
(q - 8)2