Factoring Worksheet With Examples Page 32
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50EXAMPLE
Apply Several Different Factoring Techniques
3
2
+ 15 x
- 5x - 15.
Factor 5 x
3
2
5 x
+ 15 x
- 5x - 15
Original polynomial
3
2
= 5( x
+ 3 x
- x - 3)
Factor out the GCF.
3
2
= 5[( x
- x) + (3 x
- 3)]
Group terms with common factors.
2
2
= 5[x( x
- 1) + 3( x
- 1)]
Factor each grouping.
2
2
= 5( x
- 1)(x + 3)
-
x
1 is the common factor.
2
= 5(x + 1)(x - 1)(x + 3)
-
Factor the difference of squares, x
1, into (x + 1)(x - 1).
Factor each polynomial.
3
2
3
2
3
A.
+ x
- 50x - 25
3
B.
+ 6 r
+ 11r + 6
2 x
r
Solve Equations by Factoring
You can apply the Zero Product Property to an
equation that is written as the product of factors set equal to 0.
Solve Equations by Factoring
_
9
2
In the equation y = x
-
, which is a value of x when y = 0?
16
_
_
_
9
3
9
A -
B 0
C
D
4
4
4
Read the Test Item
_
9
2
-
Factor x
as the difference of squares. Then find the values of x.
16
Solve the Test Item
_
9
When working with
2
y
= x
-
Original equation
16
a difference of two
squares, the solutions
_
9
2
0
= x
-
Replace y with 0.
will be a number
16
and its opposite.
2
(
_
)
3
_
_
_
9
3
3
2
2
Therefore, choices
0 = x
-
x
= x · x and
=
·
16
4
4
4
A and D can be
(
_
) (
_
)
eliminated because
3
3
0 =
x +
x -
Factor the difference of squares.
if one of them is a
4
4
solution then the
_
_
3
3
other is also a
0 = x +
or
0 = x -
Zero Product Property
4
4
solution.
_
_
3
3
-
= x
= x
Solve each equation.
4
4
_
_
3
3
The solutions are -
and
. The correct answer is C.
4
4
3
4
.
Which are the solutions of 18 x
= 50x?
_
_
_
_
_
_
_
5
5
5
5
5
5
5
F 0,
G -
,
H -
, 0,
J -
, 1,
3
3
3
3
3
3
3
Personal Tutor at
449
Lesson 8-5 Factoring Differences of Squares
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