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Factoring out the GCF. Objectives. To review what GCF means To practice finding the GCF of numbers, and terms with exponents To learn what factoring means To learn how to factor out the GCF from a polynomial. What is GCF?. GCF is short for Greatest Common Factor - PowerPoint PPT Presentation
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©M. Pickens 2007
Factoring out the GCFFactoring out the GCF
©M. Pickens 2007
ObjectivesObjectives
• To review what GCF means• To practice finding the GCF of numbers,
and terms with exponents• To learn what factoring means• To learn how to factor out the GCF from
a polynomial
©M. Pickens 2007
What is GCF?What is GCF?• GCF is short for Greatest Common Factor• The greatest common factor is the biggest
number that can be divided into both terms without a remainder
• Example: What is the GCF of 64 and 28?
What are all the numbers that will divide evenly into 64?1, 2, 4, 8, 16, 32,64
What are all the numbers that will divide evenly into 28?1, 2, 4, 7, 14, 28
The Greatest Common Factor of 64 and 28 is 4
©M. Pickens 2007
GCF PracticeGCF Practice
• What is the GCF of 72 and 81?
What are all the numbers that will divide evenly into 72?1, 2, 3, 4, 6, 8, 9,
What are all the numbers that will divide evenly into 81?1, 3, 9, 27, 81
The Greatest Common Factor of 72 and 81 is 9
12,18,24,36,72
©M. Pickens 2007
GCF PracticeGCF Practice
• What is the GCF of 24, 46, and 92?
What are all the numbers that will divide evenly into 24?1, 2, 3, 4, 6, 8,12, 24
What are all the numbers that will divide evenly into 46?1, 2, 23,46
What are all the numbers that will divide evenly into 92?1, 2, 4, 23,46,92
The GCF of 24, 46 and 92 is 2
©M. Pickens 2007
GCF PracticeGCF Practice• Try these on your own• Find the GCF of each set of numbers
• 1. 90, 76
• 2. 16, 40, 96
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90Factors of 76: 1, 2, 4, 19, 38, 76GCF = 2
Factors of 16: 1, 2, 4, 8, 16 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
GCF = 8
©M. Pickens 2007
GCF with variablesGCF with variables• Sometimes we want to find the GCF of terms
with variables. • First, find the GCF of the coefficients • Then find the GCF of the variables by looking
for variables in common and using the one with the smallest exponent for each variable
Example: Find the GCF of 28x3y7 and 21x2y9z
What is the GCF of the coefficients 28 and 21? 7
What variables do both terms have in common? x and yWhat are the smallest exponents for x and y? x2 and y7
The GCF is: 7x2y7
©M. Pickens 2007
GCF PracticeGCF Practice• What is the GCF of the following 3 terms?
18a3b9c 24ab4c3 30b5c8
What is the GCF of the coefficients 18, 24 and 30? 6
What variables do they all have in common? b and c
What are the smallest exponents for b and c? b4 and c1
The GCF is: 6b4c
©M. Pickens 2007
GCF PracticeGCF Practice• What is the GCF of the following 3 terms?
7de4f 25d2e4f9 35d3e5f2
What is the GCF of the coefficients 7, 25 and 35? 1
What variables do they all have in common? d, e and f
What are the smallest exponents for d, e and f?d1, e4 and f1
The GCF is: 1de4f or de4f
©M. Pickens 2007
GCF PracticeGCF Practice• Try these on your own.• Find the GCF for each set of terms
• 1. 15x4 30x2
• 2. 30m4k8r4 60m2k2 70mk5r2
15x2
10mk2
©M. Pickens 2007
What is factoring?What is factoring?
• Factoring is like un-multiplying• To find the factors of a number we find what
numbers could have been multiplied to get that number
• We learned that with the distributive property
• To factor 12x – 42 would mean to un-multiply it or break it back into 6(2x – 7)
6 (2x – 7 ) = 12x – 42
©M. Pickens 2007
Factoring ExampleFactoring Example• Factor the following as much as possible.
15x + 20• The first thing we want to do is find the GCF
of all the terms
• Then divide each term by the GCF
What is the GCF of 15x and 20? 5
5
20
5
15x 43 x These are the factors
The factored form is 5(3x + 4)You can always multiply it out
to double check your answer
©M. Pickens 2007
Factoring PracticeFactoring Practice• Factor the following: 30x3 + 14x5
What is the GCF of 30x3 and 14x5? 2x3
Divide each term by the GCF?
3
5
3
3
2
14
2
30
x
x
x
x 2715 x These are the factors
The factored form is 2x3(15 + 7x2)
©M. Pickens 2007
Factoring PracticeFactoring Practice• Factor the following: 12a2b3 + 9ab5 – 3a5b2
What is the GCF of all 3 terms? 3ab2
Divide each term by the GCF?
2
25
2
5
2
32
3
3
3
9
3
12
ab
ba
ab
ab
ab
ba 4334 abab These are the factors
The factored form is 3ab2(4ab+3b3 – a4)
©M. Pickens 2007
Factoring PracticeFactoring Practice• Factor each of the following on your own
• -30x – 45
• 27a2b3c4 + 54a5c6 + 18a4b2c
-15(2x + 3)
9a2c(3b3c3 + 6a3c5 + 2a2b2)
©M. Pickens 2007
Factoring PracticeFactoring Practice
• Factor each of the following on your own
• 18p4r – 6p3
• 7a2b3c + 9b2d2 + 5b4d7
6p3(3pr – 1)
b2(7a2bc + 9d2 + 5b2d7)
