NAME___________________________________
Math 1010:
NOTES UNIT 5.3 Common Factors and Factoring by Grouping.
OBJECTIVES:
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Terms with Common Factors
Factoring by Grouping
Factoring is the opposite of multiplication. Previously you were taught to factor integers. Factoring
an integer means to write the integer as a product of two or more integers.
In this first section we will be using the (GCF) . The common factor of two or more integers is
the greatest common factor to each integer. It is useful to express the numbers as a product of
prime factors.
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Finding the GCF of a list of Monomials
Step 1: Find the GCF of the numerical coefficients.
Step 2: Find the GCF of the variable factors.
Step 3: The product of the factors found in Steps 1 and 2 is the GCF of the
monomials.
Example 1:
Step 1: Find the GCF of the numerical coefficients.
Step 2: Find the GCF of the variable factors
Step 3: The product of the factors found in Steps 1 and 2 is the GCF of the monomials.
Example 2:
15-5x
4
y312
 12
y3 
y4 y
Example 3: 1515
Factor by Grouping
1.Identify and factor out the GCF from all four terms.
2. Group the first pair of terms and the second pair of terms. Make sure you always connect the
terms by addition. Factor out the GCF from the first pair of terms. Factor out the GCF from the
second pair of terms. (Sometimes it is necessary to factor out the opposite of the GCF.)
3. If the two terms share a common binomial factor, factor out the binomial factor
4
3
Example 4: (4u  6u )  (2u  3)
Example 5:
2w[(8w3  20w2 )  (6w  15)]