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Factoring Using the Distributive Property

Factoring Using the Distributive Property. GCF and Factor by Grouping. Review. 1) Factor GCF of 12a 2 + 16a. 12a 2 = 16a =. Use distributive property. Using GCF and Grouping to Factor a Polynomial. First, use parentheses to group terms with common factors.

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Factoring Using the Distributive Property

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  1. Factoring Using the Distributive Property GCF and Factor by Grouping

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

  3. 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.

  4. 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.

  5. 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.

  6. 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)

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

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

  9. 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.

  10. 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.

  11. 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.

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