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Math 1300
Section 4.4 Notes
1
Solving Equations by Factoring
Definition:
The
zeroproduct property
says that if
a
and
b
are numbers such that
ab
=
0, then
a
= 0 or
b
= 0 (or both).
Definition:
A
quadratic equation
is an equation that can be written as
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
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 Spring '08
 Staff
 Math, Factoring, Equations

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