When factoring, we look for greatest common factor of each term and reverse the distributive property and take out the GCF.

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1 Factoring: reversing the distributive property. The distributive property allows us to do the following: When factoring, we look for greatest common factor of each term and reverse the distributive property and take out the GCF. The GCF is Write the terms as products using the GCF factor. 3. Reverse the distributive property by factoring out the GCF. 4. Check your answer by multiplying using the distributive property. The [1]

2 The GCF is x. 2. Write the terms as products using the GCF factor. 3. Reverse the distributive property by factoring out the GCF. 4. Check your answer by multiplying using the distributive property. The The GCF is Write the terms as products using the GCF factor. 3. Reverse the distributive property by factoring out the GCF. 4. Check your answer by multiplying using the distributive property. The [2]

3 The GCF is 5y. 2. Write the terms as products using the GCF factor. 3. Reverse the distributive property by factoring out the GCF. 4. Check your answer by multiplying using the distributive property. The The GCF is 4x. 2. Write the terms as products using the GCF factor. 3. Reverse the distributive property by factoring out the GCF. 4. Check your answer by multiplying using the distributive property. The [3]

4 1. Since both terms have a negative coefficient first factor out a Find the GCF. The GCF is 2x. 3. Write the terms as products using the GCF factor. 4. Reverse the distributive property by factoring out the GCF. 5. Check your answer by multiplying using the distributive property. The 1. Since both terms have a negative coefficient first factor out a Find the GCF. The GCF is 4x. 3. Write the terms as products using the GCF factor. 4. Reverse the distributive property by factoring out the GCF. [4]

5 There is no GCF. Therefore you cannot factor this expression. Factor each polynomial. 1. GCF = b 2. Cannot be factored 3. GCF = 4. GCF = [5]

6 FACTORING OUT A COMMON BINOMIAL FACTOR Sometimes the GCF of terms is a binomial. This GCF is called a common binomial factor. Factor out a common binomial factor the same way you factor out a monomial factor. EXAMPLE: Factor Both terms have the common binomial factor of so factor it out. EXAMPLE: Factor Both terms have the common binomial factor of so factor it out. EXAMPLE: Factor Both terms have the common binomial factor of so factor it out. EXAMPLE: Factor There are no common factors so the expression cannot be factored. [6]

7 FACTORING BY GROUPING When a polynomial has four terms, you can make two groups and factor out the GCF from each group. the polynomial by grouping. Check your answer. 1. Group terms that have a common number or variable as a factor. 2. Factor out the GCF of each group. Notice that common factor. is another 3. Factor out. 4. Check your answer by multiplying. The product should be your original polynomial. the polynomial by grouping. Check your answer. 1. Group terms that have a common number or variable as a factor. 2. Factor out the GCF of each group. Notice that common factor. is another 3. Factor out. 4. Check your answer by multiplying. [7]

8 the polynomial by grouping. Check your answer. 1. Group terms that have a common number or variable as a factor. 2. Factor out the GCF of each group Check your answer by multiplying. [8]

9 FACTORING WITH OPPOSITES 1. Group terms that have a common number or variable as a factor. 2. Factor out the GCF of each group. 3. Write as 4. Simplify. is a common factor. 5. Check your answer by multiplying. 1. Group terms that have a common number or variable as a factor. 2. Factor out the GCF of each group Simplify. 4. Check your answer by multiplying. [9]

10 FACTOR EACH EXPRESSION. 1. GCF = 2. GCF = 3. GCF = 4. (The binomial factors are opposites) [10]

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