Chapter 6 Quadratic Equations By Factoring Worksheet With Answer Key - Mcgraw-Hill Page 3
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OLVING
UADRATIC
QUATIONS BY
ACTORING
ECTION
Example 3
Solving Equations by Factoring
2
Solve 2x
x
3.
The first step in the solution is to write the equation in standard form (that is, when one
side of the equation is 0). So start by adding
3 to both sides of the equation. Then,
Make sure all terms are on one side of
2
2x
x
3
0
C A U T I O N
the equation. The other side will be 0.
Consider the equation
You can now factor and solve by using the zero-product rule.
x(2x
1)
3
(2x
3)(x
1)
0
Students are sometimes
tempted to write
2x
3
0
or
x
1
0
x
3
or
2x
1
3
2x
3
x
1
This is not correct. Instead,
subtract 3 from both sides of
3
the equation as the first step
x
to write
2
2
2x
x
3
0
3
The solution set is
,
1
.
in standard form. Only now can
2
you factor and proceed as
before.
C H E C K Y O U R S E L F 3
2
Solve 3x
5x
2.
Always examine the quadratic member of an equation for common factors. It will make
your work much easier, as Example 4 illustrates.
Example 4
Solving Equations by Factoring
2
Solve 3x
3x
60
0.
First, note the common factor 3 in the quadratic member of the equation. Factoring out
the 3, we have
2
3(x
x
20)
0
Now divide both sides of the equation by 3.
2
3(x
x
20)
0
NOTE
Notice the advantage of
dividing both members by 3.
3
3
The coefficients in the
or
quadratic member become
smaller, and that member is
2
x
x
20
0
much easier to factor.
We can now factor and solve as before.
(x
5)(x
4)
0
x
5
0
or
x
4
0
x
5
x
4
or
5,
4
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