1. Solving Equations by Factoring

2. The general form of a quadratic equation is:
Solving Quadratic Equations
The general form of a quadratic
equation is:
ax2 + bx + c = 0
For example : x2 – 3x + 2 = 0

3. We’ll use the Zero-Factor Property:
Solving Quadratic Equations
We’ll use the Zero-Factor Property:
For any two numbers a and b,
If ab = 0, then a = 0 or b = 0.

4. Solve: x2 – 3x + 2 = 0 (x – 1)(x – 2) = 0 So, we know that: x – 1 = 0
Example 1:
Solve: x2 – 3x + 2 = 0
(x – 1)(x – 2) = 0
So, we know that:
x – 1 = 0 or
x – 2 = 0
x = 1 or
x = 2

5. Solve 3x2 + 6x = 0 Solution : 3x(x + 2) = 0 3x = 0 or x + 2 = 0 x = 0
Example 2:
Solve 3x2 + 6x = 0
Solution :
3x(x + 2) = 0
3x = 0 or
x + 2 = 0
x = 0 or
x = – 2

6. Solution : 5x = 6 – 6x2 6x2 + 5x – 6 = 0 (3x – 2)(2x + 3) = 0
Example 3:
Solution :
5x = 6 – 6x2
Get rid of fractions!
6x2 + 5x – 6 = 0
(3x – 2)(2x + 3) = 0
3x – 2 = 0 or
2x + 3 = 0 or

7. Solution : x(6x2 – x – 2) = 0 x(3x – 2)(2x +1) = 0 x = 0 or 3x – 2 = 0
Example 4:
Solution :
x(6x2 – x – 2) = 0
Factor out GCF!!
x(3x – 2)(2x +1) = 0
x = 0 or
3x – 2 = 0
or 2x + 1 = 0
x = 0,

8. Solving Equations by Factoring:
Write the equation with 0 on right-hand side.
Factor the left-hand side.
Set each factor equal to 0.
Solve these simpler equations.