The Greatest Common Factor And Factoring By Grouping Worksheet With Answer Key

The Greatest Common Factor And Factoring By Grouping Worksheet With Answer Key - Section 6.1

Section 6.1 The Greatest Common Factor and Factoring by Grouping

Greatest Common Factor (GCF):

 The GCF is an expression of the highest degree that divides each term of the polynomial.

 The variable part of the greatest common factor always contains the smallest power of a

variable that appears in all terms of the polynomial.

Finding GCF

 Step 1: Find the prime factorization of all integers and integer coefficients

 Step 2: List all the factors that are common to all terms, including variables

 Step 3: Choose the smallest power for each factor that is common to all terms

 Step 4: Multiply these powers to find the GCF

NOTE: If there is no common prime factor or variable, then the GCF is 1

(Example) Find the GCF for the following set of algebraic terms: {30x

y, 45x

y, 75x

}

30x

y =

2·3·5·x·x·x·x·y

2·3·5·x

45x

y =

3·3·5·x·x·x·y

·5·

75x

= 3·5·5·x·x·x·x·x·y·y =

3·5

·x

3 ∙ 5 ∙

∙

Therefore, GCF is

Negative GCF

 In my opinion, we do not need to factor out a negative GCF

 Factoring out a negative GCF is exactly same as factoring out GCF, but last step.

 Step 1: Find the prime factorization of all integers and integer coefficients

 Step 2: List all the factors that are common to all terms, including variables

 Step 3: Choose the smallest power of each factor that is common to all terms

 Step 4: Multiply these powers to find the GCF

 Step 5: Put negative sign in front of the GCF

Factoring by Grouping will be discussed with examples

Exercises

(Solution 1)

Step 1: Prime Factorization (ignore signs)

∙ 3 ∙ 3

∙ 3

∙ 2 ∙ 2

∙ 5

Step 2: List all factors that are common to all terms

Common factors to all are 2 and y

Step 3: Choose the smallest power

The smallest power for 2 is 1

The smallest power for y is 1

So, the GCF is 2 ∙

Cheon-Sig Lee

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The Greatest Common Factor And Factoring By Grouping Worksheet With Answer Key - Section 6.1

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