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Do Now. Find the GCF of each set of numbers. 34, 51 36, 72 21, 42, 56. Finding the GCF. For variables that ALL terms have in common, the GCF is always the smallest exponent that you have of each variable. 1)x 3 , x 5 2)z 4 , z 2. 3)12a 5 , 18a 2 4)18xy, 36y 2

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Do now

Do Now

Find the GCF of each set of numbers.

  • 34, 51

  • 36, 72

  • 21, 42, 56


Finding the gcf

Finding the GCF

For variables that ALL terms have in common, the GCF is always the smallest exponent that you have of each variable.

1)x3, x5

2)z4, z2


Do now

3)12a5, 18a2

4)18xy, 36y2

5)36x2y, 54 xy2z

6)12a5c7, 24a3b2c, 18a10b4c3


Factoring using the gcf

Factoring Using the GCF

Factoring with a GCF is basically the opposite of using the distributive property.

4a (3a + 4)

12a2

+ 16a


Factoring using the gcf1

Factoring Using the GCF

Now we’re going to start with:12a2 + 16a

and end up with:4a (3a + 4)

Steps:

  • Find the GCF of ALL of the terms. The GCF will be on the outside of the ( ).

  • Divide each original term by the GCF to get each term inside the ( ).

    * You always have to have the same number of terms inside the ( ) as you started with.


Do now

  • FACTOR 25a2 + 15a.

    Find the GCF and divide each term

    25a2 + 15a = 5a ( ___ + ___ )

    Check your answer by distributing.


2 factor 18x 2 12x 3

Divide each term by the GCF

18x2 - 12x3 = 6x2 ( ___ – ___ )

Check your answer by distributing.

2)Factor 18x2 – 12x3.


3 factor 28a 2 b 56abc 2

3) Factor 28a2b + 56abc2.

28a2b + 56abc2 = 28ab ( __ + ___ )

Check your answer by distributing.


4 factor 28a 2 21b 35b 2 c 2

4) Factor 28a2 + 21b – 35b2c2

28a2 + 21b - 35b2c2 = 7 ( ___ + ___ – ____ )

Check your answer by distributing.


Factor

Factor

3x2y – 27x5y3z + 18x3y7z2


Factor 16xy 2 24y 2 z 40y 2

Factor 16xy2 - 24y2z + 40y2

  • 2y2(8x – 12z + 20)

  • 4y2(4x – 6z + 10)

  • 8y2(2x - 3z + 5)

  • 8xy2z(2 – 3 + 5)


Factor 20x 2 24xy

Factor 20x2 - 24xy

  • x(20 – 24y)

  • 2x(10x – 12y)

  • 4(5x2 – 6xy)

  • 4x(5x – 6y)


Homework

Homework

Chapter 9 Packet

Pgs. 529 #’s 1 – 12


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