The Greatest Common Factor And Factoring By Grouping Worksheet With Answer Key - Section 6.1 Page 3
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4Section 6.1 The Greatest Common Factor and Factoring by Grouping
(Solution 5)
Step 1: Prime Factorization (ignore signs)
4
∙
24
∙ ∙ 2 ∙ 3
∙ 3
20
∙ ∙ 5
∙ 5
Step 2: List all factors that are common to all terms
Common factors to all are
2
and x.
Step 3: Choose the smallest power
The smallest power for 2 is 2
The smallest power for x is 2
GCF 2 ∙
4
⟹ the negative GCF is
Factoring out the negative GCF
4
24
20
4
24
20
,
,
4
4
4
(Solution 6)
Step 1: Prime Factorization (ignore signs)
12
∙
∙ 3
∙ 3
16
∙
∙ 2 ∙ 2
Step 2: List all factors that are common to all terms
Common factors to all are 2, a, and b.
Step 3: Choose the smallest power
The smallest power for 2 is 2
The smallest power for a is 1
The smallest power for b is 1
GCF 2
4
⟹ the negative GCF is
Factoring out the negative GCF
12
16
16
12
,
4
4
(Solution 7)
Step 1: Prime Factorization (ignore signs)
12
2 ∙ 2 ∙ 3
2 ∙ 3
since (x + y) is prime
Step 2: List all factors that are common to all terms
Common factors to all are (x + y).
Step 3: Choose the smallest power
The smallest power for (x + y) is 1
So, the GCF is
(x + y)
Factoring out GCF
12
12
;
Cheon-Sig Lee
Page 3
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