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TRS 82 – Day 20
Goal – Factor out the greatest common factor (GCF)
 review distributive property
 review factors and products (definitions)
 define and find the greatest common factor (GCF)
 rewrite expressions by factoring out the GCF
Review: Simplify using The Distributive Property
1. 6(z – 4) = 6z – 24
2. (3 – 7b)(-2) = -6 + 14b
3. 4(2x2 - 7) = 8x2 – 28
4. 3m(m – 6) = 3m2 – 18m
Factors are the numbers, variables or expressions you
multiply together to get another number, variable or
expression. (Something you multiply to get a product.)
Ex:
3  4  12
Ex:
3  m2  3m2
Ex:
7(4x + 5) = 28x + 35
Common factors are factors that two or more expressions have in common.
The greatest common factor is the largest common factor.
To find the greatest common factor (GCF):
1. List the prime factors of each number or expression.
(Remember that a prime number has exactly two factors: itself and one.)
2. Find all the prime factors they have in common.
3. Multiply the prime factors to get the GCF.
Consider the numbers 20, 24, 28
List the prime factors of each number:
20: 2, 2, 5
24: 2, 2, 2, 3
28: 2, 2, 7
Find the GCF of 9, 27, 45
List the prime factors of each number:
9: 3, 3
27: 3, 3, 3
45: 3, 3, 5
Find the GCF of m5, m3, m2
List the prime factors of each expression:
m5: m, m, m, m, m
m3: m, m, m
m2: m, m
Find the GCF of 9x3, 6x2y
List the prime factors:
9x3: 3, 3, x, x, x
6x2y: 2, 3, x, x, y
Find the GCF of 2b(b + 9) and 5b(b + 9)
List the prime factors:
2b(b + 9)
2, b, (b + 9)
5b(b+9)
5, b, (b + 9)
Find the GCF of k(k + 2) and 8k(k + 2)
List the prime factors:
k(k + 2)
k, (k+2)
8k(k + 2)
2, 2, 2, k, (k+2)
Our goal is to factor out the greatest common factor
(GCF).
Factoring is like taking a number or expression apart. It means to express a
number or expression as the product of its factors. It is the distributive property
in reverse.
Example:
6(z – 4) = 6z – 24
factor ∙ factor
= product
distributive property
6z – 24 = 6(z – 4)
product
= factor ∙ factor
factoring (dividing out the GCF)
To factor
1. Find the GCF of each term
2. Divide each term by the GCF and write the
expression as a product of factors
3. USE DISTRIBUTIVE PROPERTY TO CHECK WORK
Factor:
8x – 24 = 8(x - 3)
check: 8(x – 3) = 8x - 24
7x – 7 =7(x – 1)
check: 7(x – 1) = 7x - 7
5 - 10b = 5(1 – 2b)
8x2 – 28 = 4(2x2 – 7)
3m3 – 21m = 3m(m2 – 7)
8y5 – y4 – 4y2 = y2(8y3 – y2 – 4)
15k4 – 10k3 – 25k = 5k(3k3 – 2k2 – 5)
Factoring can be used to simplify fractions.
12
30
Find the GCF of each number.
Prime factorization:
12: 2, 2, 3
30: 2, 3, 5
GCF is 6
12 6  2 2


30 6  5 5
(equivalent fractions)
Simplify the fractions
6x  3
6
4 x 2  20
2
6 x  3 3(2 x  1) (2 x  1)


6
23
2
4 x 2  20 4( x 2  5)

 2( x 2  5)
2
2