Download Zero Product Property

Factor.
1) x² + 8x + 16
2) y² – 4y – 21
Zero Product Property
If two numbers multiply to zero, then
either one or both numbers has to equal
zero.
If a • b = 0 then either
a=0,
b=0,
or both a and b equal 0.
1. Solve
(x + 3) (x – 5) = 0
Using the Zero Product Property,
you know that either
x + 3 = 0 or x – 5 = 0
Solve each equation.
x = - 3 or x = 5
Solutions: {-3, 5}
2. Solve (2a + 4) (a + 7) = 0
3. Solve
(3t + 5) (t – 3) = 0
Solve
a.
b.
c.
d.
{-3, 3}
{-3, 6}
{3, 6}
{3, -6}
(y – 3) (2y + 6) = 0
Quadratic Equations
A quadratic equation is an equation that
contains a variable squared in it, and no
higher powers of the variable.
Ex:
x2 + 3x – 10 = 0
y2 – 16 = 0
6a + a2 = 16
Solving Quadratic Equations
The zero product property can be used to solve
quadratic equations.
Steps:
1) Set the equation equal to zero.
* You want the squared term to be positive
2) Factor.
3) T out.
4) Check with your calculator.
4.
2
x
+ 4x + 3 = 0
5.
2
x
+ 2x = 15
6.
a2 = -6a + 27
Solve.
1.
2.
3.
4.
{-8, 5}
{-5, 8}
{-8, -5}
{5, 8}
2
a
+ 40 = 3a
7.
2
x
–9 = 0
8.
2
x
= 36
9.
2
9r
= 16
10.
2
x
– 11x = 0
11.
2
x
= 4x
Homework
Homework 2/8 Worksheet
Review Sheet