Factoring Using the Distributive Property

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Factoring Using the Distributive Property.

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Presentation transcript:

Factoring Using the Distributive Property GCF and Factor by Grouping

Review 1) Factor GCF of 12a2 + 16a 12a2 = 16a = Use distributive property

Using GCF and Grouping to Factor a Polynomial First, use parentheses to group terms with common factors. Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.

Using GCF and Grouping to Factor a Polynomial First, use parentheses to group terms with common factors. Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.

Using GCF and Grouping to Factor a Polynomial First, use parentheses to group terms with common factors. Next, factor the GCF from each grouping. Now, Distributive Property…. Group both GCF’s. and bring down one of the other ( ) since they’re both the same.

Using the Additive Inverse Property to Factor Polynomials. When factor by grouping, it is often helpful to be able to recognize binomials that are additive inverses. 7 – y is y – 7 By rewriting 7 – y as -1(y – 7) 8 – x is x – 8 By rewriting 8 – x as -1(x – 8)

Factor using the Additive Inverse Property. Notice the Additive Inverses Now we have the same thing in both ( ), so put your answer together.

Factor using the Additive Inverse Property. Notice the Additive Inverses Now we have the same thing in both ( ), so put your answer together.

There needs to be a + here so change the minus to a +(-15x) Now group your common terms. Factor out each sets GCF. Since the first term is negative, factor out a negative number. Now, fix your double sign and put your answer together.

There needs to be a + here so change the minus to a +(-12a) Now group your common terms. Factor out each sets GCF. Since the first term is negative, factor out a negative number. Now, fix your double sign and put your answer together.

Summary A polynomial can be factored by grouping if ALL of the following situations exist. There are four or more terms. Terms with common factors can be grouped together. The two common binomial factors are identical or are additive inverses of each other.