1. X-box Factoring

2. 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:
General form of a quadratic equation
Dividing a polynomial by a monomial using the box method

3. Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)= -30 x -5
-15 2
-13 2x
-10 +2
3x2 -13x -10 = (x-5)(3x+2)

4. First and Last Coefficients
Factor the x-box way
y = ax2 + bx + c
Base 1
Base 2
Product
ac=mn
First and Last Coefficients
1st Term
Factor n
GCF n m
Middle
Last term
Factor m
b=m+n
Sum
Height

5. Examples Factor using the x-box method. 1. 6x2 + 7x +2 3x 2 6x2 4x 2x12 7
6x2 4x 3x 2x 3 4 1
Solution: 6x2 + 7x –2 = (x + 2)(x +1)

6. 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)

7. Examples continued 3. 2x2 - 5x - 7 2x -7 x 2x2 -7x 2x -7
a) b) 2x -7
-14 -5 x
2x2 -7x
2x -7 +1
Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

8. Examples continued 3. 15x2 + 7x - 2 3x +2 5x 15x2 10x -3x -2
-30 7 5x
15x2 10x
-3x -2 -1
Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

9. Independent Practice
Do the worksheet using the x-box method. Show all your work to receive credit– don’t forget to check by multiplying!

10. Factor the x-box way (3)(-10)= -30 x -5 3x 3x2 -15x -15 2 -13 2x +2