1. Warm – Up # 9
Factor the following:
3x2 – 2x – 5
4x2 + 20x + 25

2. Solving Quadratic Equations
What happens when we solve for x after we factor a trinomial?

3. Vocabulary:
Quadratic Equation – any equation where 2 is the highest exponent.
Standard form of a quadratic equation -

4. The solutions(roots) of the equation are 3 and - 6
The zero-product law is used to solve an equation when one side is zero and the other side is a product of polynomial factors
For example: m · n = 0, then m = 0 or n = 0. The solutions of such an equation are also called roots.
Example:
(x-3)(x+6) = 0
X - 3 = or x + 6 = 0
X = or x = - 6
The solutions(roots) of the equation are 3 and - 6

5. Examples: (k + 1)(k – 5) = 0 (a + 1)(a + 2) = 0 (4k + 5)(k + 1) = 0
4. (2m + 3)(4m + 3) = 0

6. Solve an equation by factoring:
6x2 + 12x = 0
6x2 + 12x = (Write the original equation)
6x(x + 2) = (Factor left side)
6x = or x + 2 = 0 (Zero-product property)
X = or x = (Solve for x)
The solutions of the equation are 0 and – 2.

7. Practice
1. b2 + 14b = 0
2. 24k k = 0

8. Examples:

9. What if we have a problem that looks like this…
What should we do??

10. Or like this…
9p2 -36 = 0

11. ~ Review~