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Section 4.1  Greatest Common Factor and Factoring by Grouping
(Review) Factoring
Definition:
A
factor
is a number, variable, monomial, or polynomial which is multiplied by
another number, variable, monomial, or polynomial to obtain a product.
1.
List all the possible factors of the following numbers:
a.
12
b.
32
c.
19
d.
45
In the above, the number 19 is an example of a ____________ number because its only positive
factors are one and itself
.
(Review) Greatest Common Factor
Definition:
The
greatest common factor
of two or more numbers is the largest number that
divides (goes into) the given numbers with a remainder of zero.
2.
Find the GCF (greatest common factor) of the following numbers:
a.
36 and 54
b.
15 and 60
c.
21, 42, and 63
d.
28 and 39
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Greatest Common Factor of Polynomials
In order to find the GCF of two or more monomials,
I.
Find the GCF of the coefficients;
II. Find the GCF of the variables;
III. Rewrite the GCF as a product of the GCF of the coefficients times the GCF of the variables.
Examples:
1.
Find the GCF of
x
4
and
x
7
.
Step I:
The only coefficients are 1’s, so this is the GCF of the coefficients.
Step II:
Rewrite the two monomials as products of
x
s without using exponents:
x
4
=
x
·
x
·
x
·
x
x
7
=
x
·
x
·
x
·
x
·
x
·
x
·
x
Since each monomial has 4
x
s in it, the GCF of the variables is
x
4
.
Step III: The GCF of
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 Spring '08
 Staff
 Algebra, Factoring, Multiplication, GCF

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