Algebra I
Module 3
Lesson 8: Zero Product Property
Name
Period
Date
Today is huge. Today is monumental. Everything we have been working on for the past
three weeks has led to this very moment. We can finally answer the question that has been
on your mind for years. How do we solve a quadratic equation?
We’ve spent years solving linear equations. In fact, you’ve gotten quite good at solving
them. Try this one…
#1
Solve for x.
3(x + 5) – 7 = 17
See? Not that tricky. But what if the equation looked like 3(x2 + 5) – 7 = 17 ? Now, we are
not getting into something that crazy…not yet at least…but how do we solve an equation
where there is an x2 in it?
#2
For each of the following number sentences, insert values into each blank space to
make the statement true. You can only use the same number once for each number
sentence.
_________ • _________ = 24
_________ •_________ •_________ = 36
_________ •_________ •_________ •_________ = 48
_________ •_________ = 0
_________ •_________ = 17
_________ •_________ •_________ = 0
_________ •_________ •_________ •_________ •_________ •_________ •_________ = 0
Which of the number sentences were easiest to fill in? Explain why you feel this way.
The reason the last three number sentences seemed so much easier is because of the
Zero Product Property.
The Zero Product Property states that when you are multiplying two (or more) terms and
the product of those terms is equal to zero, then one (or both) of those terms MUST equal
zero.
This is HUGE! This will allow us to solve equations where there is an x2 term using all the
factoring techniques we’ve learned over the past weeks.
#3
Solve the following equations by setting each term equal to zero.
(x – 5)(x + 2) = 0
(x – 7)(x + 2) = 0
x(x + 2) = 0
(x + 3)(x – 3) = 0
(2x + 5)(x – 1) = 0
(2x – 9)(3x + 4) = 0