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Objectives The student will be able to:

Objectives The student will be able to:. Factor by GROUPING still using the greatest common factor (GCF). Review: What is the GCF of 14a 2 and 21a?. 7a Let’s go one step further… 1) FACTOR 45a 2 + 9a. Find the GCF and divide each term 45a 2 + 9a = 9a ( ___ + ___ )

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Objectives The student will be able to:

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  1. ObjectivesThe student will be able to: Factor by GROUPING still using the greatest common factor (GCF).

  2. Review: What is the GCF of 14a2 and 21a? 7a Let’s go one step further… 1) FACTOR 45a2 + 9a. Find the GCF and divide each term 45a2 + 9a = 9a( ___ + ___ ) Check your answer by distributing. 5a 1

  3. Group using parentheses. (12ac + 21ad) +(8bc + 14bd) Find the GCF of each group 12ac + 21ad = 3a( ___ + ___ ) 8bc + 14bd = 2a ( ___ + ___ ) Do you notice anything? The common factor of the original polynomial is the binomial (4a + 7d) 2) Factor 12ac + 21ad +8bc +14bd. 4c 7d 4c 7d

  4. So…here is our factorization 3a(4c + 7d) + 2c(4c + 7d) (3a + 2c) (4c + 7d)

  5. Factor 6x2y + 9xyz + 4xy2 + 6y2z

  6. Factor 49m + 21m2 + 35m3n + 15m2n3

  7. If Numbers like 5 & -5 are opposites then… Numbers are defined as opposites because when added their sum is 0. terms like (x – 1) and (1 – x) are opposites. Add them and see!

  8. Factor 15x – 3xy + 4y - 20 (15x – 3xy)+(4y – 20) 3x(5 – y) + 4(y – 5) Let’s look at (5 – y) for a second… (5 – y) = (-y + 5) right? So…(-y + 5) = -(y – 5)

  9. Getting back to our factorization… Since (5 – y) = -(y – 5) 3x(5 – y) + 4(y – 5) now becomes -3x(y – 5) + 4(y – 5) Which can then be simplified to (4 – 3x)(y – 5) Or (-3x + 4)(y – 5)

  10. Factor a2 - ab – 7b + 7a

  11. Last one!3a2 - 2ab + 10b - 15a

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