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Do Now:

Do Now:. Write the standard form of an equation of a line passing through (-4,3) with a slope of -2. Write the equation in standard form with integer coefficients y = -1/3x - 4. Do Now:. Worksheet – Match the correct bottle with its graph. Factoring Using the Distributive Property.

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Do Now:

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  1. Do Now: Write the standard form of an equation of a line passing through (-4,3) with a slope of -2. Write the equation in standard form with integer coefficients y = -1/3x - 4

  2. Do Now: Worksheet – Match the correct bottle with its graph

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

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

  5. PRIME POLYNOMIALS A POLYNOMIAL IS PRIME IF IT IS NOT THE PRODUCT OF POLYNOMIALS HAVING INTEGER COEFFICIENTS. TO FACTOR A PLYNOMIAL COMPLETLEY, WRITE IT AS THE PRODUCT OF MONOMIALS PRIME FACTORS WITH AT LEAST TWO TERMS

  6. TELL WHETHER THE POLYNOMIAL IS FACTORED COMPLETELY 2X2 + 8 = 2(X2 + 4) YES, BECAUSE X2 + 4 CANNOT BE FACTORED USING INTEGER COEFFICIENTS 2X2 – 8 = 2(X2 – 4) NO, BECAUSE X2 – 4 CAN BE FACTORED AS (X+2)(X-2)

  7. 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.

  8. 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.

  9. 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.

  10. 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)

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

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

  13. 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.

  14. 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.

  15. 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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