Factoring Worksheet With Examples Page 11
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50Factoring by Grouping
A polynomial can be factored by grouping if all of the following
Words
situations exist.
• There are four or more terms.
• Terms with common factors can be grouped together.
• The two common binomial factors are identical or are additive inverses
of each other.
ax + bx + ay + by = x(a + b) + y(a + b)
Symbols
= (a + b)(x + y)
Solve Equations by Factoring
Some equations can be solved by factoring.
Consider the following products.
6(0) = 0
0(-3) = 0
(5 - 5)(0) = 0
-2(-3 + 3) = 0
Notice that in each case, at least one of the factors is zero. These examples
illustrate the Zero Product Property.
Zero Product
Zero Product Property
Property
If the product of two
Word
If the product of two factors is 0, then at least one of the factors
factors is equal to a
must be 0.
nonzero value, then
you cannot use the
For any real numbers a and b, if ab = 0, then either a = 0, b = 0,
Symbols
Zero Product Property.
or both a and b equal zero.
You must first multiply
all the factors, and then
put all the terms on
The solutions of an equation are called the roots of the equation.
one side of the
equation, with zero on
the other. Then you
EXAMPLE
Solve an Equation
must factor the new
expression and use the
Zero Product Property.
Solve each equation. Check the solutions.
a. (d - 5)(3d + 4) = 0
If (d - 5)(3d + 4) = 0, then according to the Zero Product Property either
d - 5 = 0 or 3d + 4 = 0.
(d - 5)(3d + 4) = 0
Original equation
d - 5 = 0 or 3d + 4 = 0
Set each factor equal to zero.
d = 5
3d = -4
Solve each equation.
_
4
d = -
3
_
4
The roots are 5 and -
.
3
_
4
CHECK
Substitute 5 and -
for d in the original equation.
3
-
+ 4) = 0
-
+ 4) = 0
(d
5)(3d
(d
5)(3d
_
_
⎡
⎤
⎡
⎤
(
4
)
(
4
)
(5
-
5)[3(5)
+ 4]
0
⎢
-
- 5
⎢
3
-
+ 4
0
⎣
⎦
⎣
⎦
3
3
(
_
)
19
(0)(19)
0
-
(0)
0
3
0 = 0
0 = 0
428
Chapter 8 Factoring
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education