Chapter 6 Quadratic Equations By Factoring Worksheet With Answer Key - Mcgraw-Hill Page 2
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HAPTER
OLYNOMIALS AND
OLYNOMIAL
UNCTIONS
Quadratic equations can be checked in the same way as linear equations were checked:
by substitution. For instance, if x
6, we have
2
6
3 6
18
0
36
18
18
0
0
0
which is a true statement. We leave it to you to check the solution of
3.
C H E C K Y O U R S E L F 1
2
Solve x
9x
20
0.
Other factoring techniques are also used in solving quadratic equations. Example 2
illustrates this concept.
Example 2
Solving Equations by Factoring
2
(a) Solve x
5x
0.
Again, factor the left side of the equation and apply the zero-product principle.
x(x
5)
0
C A U T I O N
A common mistake is to forget
Now
the statement x
0 when you
are solving equations of this
x
0
or
x
5
0
type. Be sure to include both
x
5
solutions in the solution set.
The two solutions are 0 and 5. The solution set is 0, 5 .
2
(b) Solve x
9
0.
Factoring yields
(x
3)(x
3)
0
x
3
0
or
x
3
0
x
3
x
3
The solution set is
3, 3 , which may be written as
3 .
NOTE
The symbol
is read
“plus or minus.”
C H E C K Y O U R S E L F 2
Solve by factoring.
2
2
(a) x
8x
0
(b) x
16
0
Example 3 illustrates a crucial point. Our solution technique depends on the zero-
product rule, which means that the product of factors must be equal to 0. The importance
of this is shown now.
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