1. Solving Quadratic Equations by Factoring

2. X- Box
Product a∙c
factors
factors
Sum b

3. 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

4. Solve the x-box way Example: Solve 3x2 -13x -10 = 0 by factoring. x -5
(3)(-10)=
-30 3x
3x2
-15x
-15 2
-13 +2 2x
-10
3x2 -13x -10 = 0 (x-5)(3x+2) = 0
X = 5, -2/3

5. First and Last Coefficients
FACTOR the x-box way
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

6. Examples Solve using the x-box method. 1. x2 + 4x – 12 = 0 x +6 x
-12 4 x 6x 6 -2 -2
-2x
-12
Solution: x2 + 4x – 12 = (x + 6)(x - 2) = x = -6,2

7. Examples 2. x2 - 9x + 20 = 0 x -4 x Solution: x2 - 9x + 20 = 0 20 -9 x x²
-4x -5
-5x 20
Solution: x2 - 9x + 20 = 0
(x - 4)(x - 5) = 0
x = 4, 5

8. Examples 3. 2x2 - 5x – 7 = 0 2x -7 x Solution: 2x2 - 5x – 7 = 0
-14 -5 x
-7x
2x² +1 2x -7
Solution: 2x2 - 5x – 7 = 0
(2x - 7)(x + 1) = x = 7/2, -1

9. Examples 4. 15x2 + 7x – 2 = 0 3x +2 5x Solution: 15x2 + 7x – 2 = 0
-30 7 5x
15x²
10x -1
-3x -2
Solution: 15x2 + 7x – 2 = 0
(3x + 2)(5x - 1) = x = -2/3, 1/5