1. Solving Equations by Factoring

2. Essential Question
How do I solve equations by factoring?

3. Solving by Factoring (x - 2) (x - 4) = 0
What can you tell me about ONE of these factors?
One MUST be ZERO, in order for the product to be ZERO.
(x – 2)(x – 4) = 0
Either x – 2 = or x – 4 = 0
So…to solve the equation, we are going to set each factor equal to 0!!

4. Steps for Solving * First factor the polynomial completely!
* Use GCF, Difference of Squares, Grouping, and Reverse FOIL until the problem is completely factored!
(You already know how to do all of this!!)
* Then, set each individual factor equal to 0 and solve!

5. Example 1 Solve! x2 + 5x + 6 = 0 (x + 2)(x + 3) = 0 x + 3 = 0OR
x = -3
x = -2
Solution: x = -2 or -3

6. Example 2 Solve! x2 + x – 20 = 0 (x + 5)(x – 4) = 0 x - 4 = 0OR
x = 4
x = -5
Solution: x = -5 or 4

7. Example 3 Solve! 3x2 + 8x + 4 = 0 (3x + 2)(x + 2) = 0 x + 2 = 0OR
x = -2
x = -2/3
Solution: x = -2/3 or -2

8. Example 4 Solve. x2 – 9 = 0 (x + 3)(x – 3) = 0 x - 3 = 0 x + 3 = 0 OR
Solution: x = -3 or 3

9. Example 5
Solve!
6x2 – 2x – 8 = 0
2(3x2 – x – 4) = 0
2(3x – 4)(x + 1) = 0
**We don’t have to consider 2 as a factor since it is a constant and there is no variable!
x + 1 = 0
3x - 4 = 0 OR
x = -1
x = 4/3
Solution: x = 4/3 or -1

10. Example 6 x + 1 = 0 x - 6 = 0 OR x = -1 x = 6 Solution: x = 6 or -1
Solve!
x2 – 5x = 6
x2 – 5x – 6 = 0
(x – 6)(x + 1)= 0
You must have a 0 on the right side of your equation!
x + 1 = 0
x - 6 = 0 OR
x = -1
x = 6
Solution: x = 6 or -1

11. You Try! Solve! x2 – 49 = 0 x2 + 6x = -9 x2 + x – 12 = 0
3. x = -4 or 3
4. x= 3/2 or -3

12. Other names for solving by factoring…
The directions may ask you to…
Solve
Find the zeros
Find the roots
Find the solution
These are all names for the same thing….”solve by factoring.”