Objective 14 – Null Factor Law and Solving Quadratic Equations:
What is the null factor law?
Given that : AB  0
Then either A  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  0
( x  9)( x  8)  0
Now we will apply the null factor law: (  means therefore )
x 2  x  72  0
( x  9)( x  8)  0
 either ( x  9)  0 or ( x  8)  0
To finish the problem we must solve for x in each equation:
x 2  x  72  0
( x  9)( x  8)  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
(9) 2  (9)  72  0
81  81  0
00
This is true
let x  8
and
x 2  x  72  0
(8) 2  (8)  72  0
72  72  0
00
This is true
More Examples:
a)
x2  x  0
x( x  1)  0
 either x  0 or x  1  0
x  0 or x  1
9x3  x  0
b)
c)
( x)(9 x 2  1)  0
( x)(3x  1)(3x  1)  0
 either x  0 or 3x  1  0 or 3x  1  0
1
1
x  0 or x  
or x 
3
3
x 2  12 x  11  0
( x  11)( x  1)  0
 either x  11  0 or x  1  0
x  -11 or x  1
2x 2  x  6  0
2 x 2  4 x  3x  6  0
(2 x)( x  2)  3( x  2)  0
d)
( x  2)( 2 x  3)  0
 either x  2  0 or 2 x  3  0
x  -2 or
x
3
2
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Objective 14 – Null Factor Law and Solving Quadratic Equations: