1. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Vocabulary
Zero-Product
Property
Let a and b be real numbers If ab = 0, then = 0 or = 0. a b

2. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Example 1
Use the zero-product property
Solve
Write original equation.
______________ property.
Zero-product
x = ______
or x = _____
Solve for x.
5 and -4
The solutions of the equation are ______________.
Check. Substitute each solution into the original equation to check.

3. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Checkpoint. Complete the following exercises.

4. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Methods of Factoring
Binomial
Trinomial
4 or more terms
GCF
GCF
GCF
Difference of Squares
Perfect Square Trinomial
Grouping
Two Binomials (Shortcut)
Two Binomials (cross)

5. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Example 2
Solve an equation by factoring
Solve
Write original equation.
Factor left side. (GCF)
Zero-product property.
x = ______
or x = _____
Solve for x.
0 and -5
The solutions of the equation are ______________.

6. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Example 3
Solve an equation by factoring
Solve
Write original equation.
24b
Subtract _____ from each side.
Factor left side. (GCF)
Zero-product property.
x = ______
or x = _____
Solve for b.
0 and 8/3
The solutions of the equation are ______________.

7. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Example 3
Solve a multi-step problem
Fountain: A fountain sprays water from the ground into the air with an initial velocity of 20 feet per second. After how many seconds does it land on the ground?
Solution
Step 1 Write a model for the water’s height above ground.
Vertical motion model.
v = ___ and s = ___.
Simplify.

8. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Example 3
Solve a multi-step problem
Fountain: A fountain sprays water from the ground into the air with an initial velocity of 20 feet per second. After how many seconds does it land on the ground?
Solution
Step 2 Substitute __ for h. When the water lands, its height above the ground is __ feet. Solve for t.
Substitute __ for h.
Factor right side.
Zero-product property.
t = ______
or t = _____
Solve for x.
1.25
The water lands on the ground ______ after it is sprayed.

9. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Checkpoint. Complete the following exercises.

10. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Checkpoint. Complete the following exercises.

11. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form
Checkpoint. Complete the following exercises.
In Example 4, suppose the initial velocity is 18 feet per second. After how many seconds does the water land on the ground?
1.125
The water lands on the ground ______ after it is sprayed.

12. Solve Equations in Factored Form
2.5
Solve Equations in Factored Form