Math 1300
Section 4.4 Notes
1
Solving Equations by Factoring
Definition:
The zeroproduct property
says that if
a
and
b
are numbers and if
ab
= 0, then
a
= 0 or
b
= 0 (or both).
Definition:
A quadratic equation
is an equation that can be written
ax
2
+
bx
+
c
= 0,
where
a
,
b
, and
c
are numbers and
a
≠
0.
Solving Quadratic Equations
To solve a quadratic equation, we must find all possible values for
x
that make
ax
2
+
bx
+
c
= 0.
Factoring is usually a helpful way to solve quadratic equations.
To use factoring,
move all nonzero terms to one side of the equal sign so that the other side is zero.
Then
use the zeroproduct property.
Examples:
1.
Solve the equation
x
2
– 5
x
– 24 = 0.
Only the lefthand side (LHS) of the equation has nonzero terms, so no movement
of terms is necessary.
Factor the LHS and use the zeroproduct property (ZPP):
x
2
– 5
x
– 24 = 0
Factor
:
(
x
+ 3)(
x
– 8) = 0
ZPP
:
x
+ 3 = 0
or
x
– 8 = 0
Solve for
x
:
x
= –3
or
x
= 8
2.
Solve 2
x
2
+ 18
x
– 72 = 0 for
x
.
All nonzero terms are on the LHS, so no movement of terms is needed.
2
x
2
+ 18
x
– 72
Factor
:
2(
x
+ 12)(
x
– 3) = 0
ZPP
:
x
+ 12 = 0
or
x
– 3 = 0 (Note: 2
≠
0, so we don’t write it)
Solve for
x
:
x
= –12
or
x
= 3
3.
Solve the equation 6
x
2
– 27
x
= –12.
This equation has nonzero terms on both sides of the equal sign.
To make it
possible to solve, move the –12 to the LHS by adding 12 to both sides:
6
x
2
– 27
x
+ 12 = 0
Factor
:
3(2
x
– 1)(
x
– 4) = 0
ZPP
:
2
x
– 1 = 0
or
x
– 4 = 0 (Note: 3
≠
0)
Solve for
x
:
x
= ½
or
x
= 4
4.
Solve 16
x
2
= 1.
Subtract 1 from both sides
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 Spring '08
 Staff
 Math, Factoring, Equations, Quadratic equation, Elementary algebra, ZPP

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