1. Factoring Quadratic Equations

2. What are Quadratic Equations?
A quadratic equation is an equation which:
y = x2
y = x2 + 2
y = x2 + x – 4
y = x2 + 2x – 3
The highest exponent is 2
All of these equations contain a x2 term therefore they are called:
Quadratic Equations

3. Which of the following are
Quadratic Equations?
y = x + 3
It’s degree is 2
y = x2
....WHY?
y = 2x – 4
It’s degree is 2
y = x2 + 2x – 3
….WHY?

4. Find the factors of c that add to b
Factoring Quadratic Equations
Remember:
Quadratic Equations have a degree of 2
Quadratics
ax2 + bx + c
Find the factors of c that add to b
“Factors” are the numbers you multiply to get another number
1 x 6 and 2 x 3
The (+) factors of 6 are:
The (-) factors of 6 are:
-1 x -6 and -2 x -3

5. How to Factor Quadratic Equations
Example x2 + x + 7 7 12 12
1 x 12 = x -12 = 12
2 x 6 = x -6 = 12
3 x 4 = x -4 = 12
Write down all the factor pairs of ___.
(x )(x )
What goes with the x? 1
Positive Negative
From this list, choose the pair that adds up to ___ 2
3 + 4 = 7
(x + 3)(x + 4)
(x + )(x + ) 3
Put these numbers into brackets

6. (x + 3) (x + 4) x(x + 4) + 3(x + 4) x(x) + x(4) + 3(x) + 3(4)
PROOF:
x2 + 7x + 12 = (x + 3) (x + 4)
(x + 3) (x + 4)
x(x + 4) + 3(x + 4)
x(x) + x(4) + 3(x) + 3(4)
x2 + 4x + 3x + 12
x2 + 7x + 12
Factor:
Factor:
Combine like terms:

7. How to Factor Quadratic Equations
Example x2 + x + 6 6
(x )(x )
What goes with the x? 8 8
1 x 8 = x -8 = 8
2 x 4 = x -4 = 8
Write down all the factor pairs of ___. 1
Positive Negative
From this list, choose the pair that adds up to ___ 2
2 + 4 = 6 3
Put these numbers into brackets
(x + 2)(x + 4)

8. How to Factor Quadratic Equations
Example x2 x -3 -3 -4 -4
-1 x 4 = x 2 = -4
1 x -4 = x -2 = -4
Write down all the factor pairs of ___. 1
(x )(x )
What goes with the x?
From this list, choose the pair that adds up to ___ 2
= -3 3
Put these numbers into brackets
(x - 4)(x + 1)

9. 1 x2 + 5x + 6 2 x2 - x – 6 3 x2 + 8x + 12 4 x2 + x – 12 5 x2 - 8x + 157
x2 - 3x – 18 8
x2 - 10x – 24 9
x2 + 8x + 16 10
x2 - 4x – 60

10. 1 x2 + 5x + 6 (x + 3)(x + 2) 2 x2 - x – 6 (x – 3)(x + 2) 34
x2 + x – 12
(x – 3)(x + 4) 5
x2 - 8x + 15
(x – 3)(x – 5) 6
x2 + 3x – 21
(x + 7)(x – 4) 7
x2 - 3x – 18
(x – 6)(x + 3) 8
x2 - 10x – 24
(x - 12)(x + 2) 9
x2 + 8x + 16
(x + 4)(x + 4) 10
x2 - 4x – 60
(x - 10)(x + 4)

11. (x )(x )
What goes with the x?

12. (x - 3) (x - 2) x(x - 2) -3(x - 2) x(x) + x(-2) - 3(x) - 3(-2)
Factor the following:
x2 - 5x + 6 =
Solution:
x2 - 5x + 6 = (x - 3) (x - 2)
(x - 3) (x - 2)
x(x - 2) -3(x - 2)
x(x) + x(-2) - 3(x) - 3(-2)
x2 - 2x - 3x + 6
x2 - 5x + 6
Factor:
Factor:
Combine like terms: