Download Introduction to factoring

Introduction to factoring
*Factors
*Greatest common factor
*prime and composite
*Factoring by distribution
Factors
• Numbers that are multiplied together
***calculator trick*****
• Divide evenly into a product
Put the number in y =
List all the factors of:
nd
48 /x
64
14
11
1
14
2
7
1
11
press 2
64
48
1
48
1
64
2
24
2
32
3
16
4
16
4
12
8
8
6
8
graph
• Prime Numbers – numbers greater than
one that have only two factors, 1 and itself
• Composite Numbers – numbers greater
than one that have more than two factors,
are not prime
14
11
1
14
2
7
Composite
1
11
Prime
64
48
1
48
1
64
2
24
2
32
3
16
4
16
4
12
8
8
6
8
Composite
Composite
• Greatest Common Factor GCF –
• The largest number that divides evenly
into two or more numbers.
What is the GCF of 14 and 11? 1
48 and 64? 16
14
11
1
14
2
7
1
11
64
48
1
48
1
64
2
24
2
32
3
16
4
16
4
12
8
8
6
8
***Calculator Trick****
To find the GCF of 2
positive numbers.
MATH
gcd(
NUM,
,
) enter
What if we throw in some
variables?
Find the GCF
2
14 x and 28x
3
24 x y and 32x
14x
14
88x
3
1st find GCF of the numbers
2nd list variables they have in common
3rd use the lowest exponent
3
What if we throw in some
variables?
Find the GCF
5
2
66 x y and 28x y
3
2
7
3
99 x y and 44x y
2
22xxyy
2
11xy
11x y
11
4
1st find GCF of the numbers
2nd list variables they have in common
3rd use the lowest exponent
4
Distribution
Simplify:
3x( x  7)  3x  21x
2
What are the two factors?
3x and x+7
What are the two things being multiplied ?
Factoring—taking a product and splitting it
up into its factors
*un-distributing the number
Factoring by Distribution
3x  21
2
• Factor
3x  21
2
x 7)
GCF
3(
2
Does it check out ?
Yes
Steps to factoring
1. Write the GCF
2. Open parentheses
3. Divide polynomial by
the GCF to find the
other factor
4. To check, multiply
the two factors to
see if you get the
original product
Factoring by Distribution
12 x  54 x
2
• Factor
12 x  54 x
( 2x 9)
GCF
6x
2
Does it check out ?
Yes
Steps to factoring
1. Write the GCF
2. Open parentheses
3. Divide polynomial by
the GCF to find the
other factor
4. To check, multiply
the two factors to
see if you get the
original product
The X game
Find two numbers the multiply to get the top
number, but also add together to get
the bottom number
Multiply
33
3
Add
List the factors of 33
11
14
1
33
3
11
Which pair adds
together to get 14?
The X game
Find two numbers the multiply to get the top
number, but also add together to get
the bottom number
List the factors of 72
Multiply
-72
12
Add
-6
6
Keep in mind, in order to get -72, One
of our pair will have to be negative
1
72
2
36
3
24
4
18
6
12
8
9
The X game
Find two numbers the multiply to get the top
number, but also add together to get
the bottom number
List the factors of 24
Multiply
24
-8
Add
-3
-11
1
24
2
12
3
8
4
6
Keep in mind, in order to get 24, both of our pair will
have to be negative, or both positive