Objective 14 – Null Factor Law and Solving Quadratic Equations:
What is the null factor law?
Given that
Then either
: AB
A


0
0 or B

0
Why is this important to know?
We will use the null factor law to solve quadratic equations.
Ex: Solve for x: x
2  x

72

0
In this problem it is hard to isolate x. However if we factor the left hand side of the equation we create a situation where we are multiplying two things together that equals zero: x
2  x

72

( x

9 )( x

8 )
0

0
Now we will apply the null factor law: (
 means therefore x
2  x

72

0
( x
 either

9 )( x
( x

9 )

8 )

0

0 or ( x

8 )

0
)
To finish the problem we must solve for x in each equation: x
2  x

72

( x

9 )( x

8 )
0

0
 either ( x

9 )

0 or ( x

8 )

0 x
 
9 or x

8
What do the answers x
 
9 and x

8 mean to the problem? x
 
9 and x

8 are the values of x that make the equation true let x
 
9 x
2  x

72

0 let x

8 x
2  x

72

0
(

9 )
2 
(

9 )
81

81

0

72

0
0

0 This is true and
( 8 )
2 
( 8 )

72
72

72

0

0
0

0 This is true

More Examples: x
2  x

0 x ( x a)
 either x


1 )

0 or x
0

1

0 x

0 or x
 
1
9 x
3  x

0
( x )( 9 x
2 
1 )

0 b) ( x )( 3 x
 either x

1 )( 3 x

1 )

0 or 3 x

1


0
0 or 3 x

1

0 x

0 or x
 
1
3 or x

1
3 x
2 
12 x

11

0
( c)
 either x x

11


11 )( x

1 )
0 or x

0

1
 x

-11 or x
 
1
0
2 x
2  x

6

0
2 x
2 
4 x

3 x

6

0 d)
( 2 x )( x

( x
2

2 )( 2 x
)


3
3 ( x
)


2 )

0
0
 either x

2

0 or 2 x

3

0 x

-2 or x

3
2