1. Objective
SWBAT solve polynomial equations in factored form.

4. Section 9.4 “Solve Polynomial Equations in Factored Form”
Zero-Product Property
If ab = 0, then a = 0 or b = 0.
The zero-product property is used to solve an equation when one side of the equation is ZERO and the other side is the product of polynomial factors.
(x – 4)(x + 2) = 0
The solutions of such
an equation are called
ROOTS.
x + 2 = 0
x – 4 = 0
x = -2
x = 4

5. Example 1A: Use the Zero Product Property
Use the Zero Product Property to solve the equation. Check your answer.
(x – 7)(x + 2) = 0
Use the Zero Product Property.
x – 7 = 0 or x + 2 = 0
Solve each equation.
x = 7 or x = –2
The solutions are 7 and –2.

6. Example 1B: Use the Zero Product Property
Use the Zero Product Property to solve each equation. Check your answer.
(x – 2)(x) = 0
(x)(x – 2) = 0
Use the Zero Product Property.
x = 0 or x – 2 = 0
Solve the second equation.
x = 2
The solutions are 0 and 2.

7. Use the Zero Product Property to solve the equation. Check your answer.
(x + 4)(x – 3) = 0
Use the Zero Product Property.
x + 4 = 0 or x – 3 = 0
x = –4 or x = 3
Solve each equation.
The solutions are –4 and 3.

8. Solve the equations
(x – 5)(x + 1) = 0
(2x – 3)(4x + 1) = 0

9. Using the Zero Product Property
Solve the equation (x – 1)(x + 7) = 0

10. You try:
Solve the equation (z – 6)(z + 6) = 0.

11. Try this one:
Solve the equation (x – 4)2 = 0