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Warm UP!. EQ: What are ways we can factor polynomials? . Factor the GCF. How can we factor the GCF out of a Polynomial???. What do these have in common??. ALL ANIMALS. What do these have in common??. ALL FLY. What is the greatest common factor??. 36. 24. The number 12.

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Warm UP!

EQ: What are ways we can factor polynomials?


Factor the GCF

How can we factor the GCF out of a Polynomial???


What do these have in common??

ALL ANIMALS


What do these have in common??

ALL FLY


What is the greatest common factor??

36

24

The number 12


What is the greatest common factor??

5a

35

The number 5


What is the greatest common factor??

3y

-8xy

y


What is the greatest common factor??

-11x

22x2

11x


What is the greatest common factor??

-4x6-x4-2x2

-x2


Always look for a Greatest Common Factor 1st.

Factor 4x + 6y

What is their greatest common factor?

= 2( )

2x

+ 3y


Factor

3y – 8xy

What is their GCF?

= y( )

– 8x

3

2a3 – 6ab2

= 2a( )

a2

– 3b2


Factor

2h2k + 2k

What is their GCF?

= 2k( )

+ 1

h2

6uv + 9v2

= 3v( )

2u

+ 3v


Factor

4x3 + 20x2 + 24x

What is their GCF?

= 4x( )

+ 5x

+ 6

x2


Factor

6x3 + 21x2 + 9x

What is their GCF?

= 3x( )

+ 7x

+ 3

2x2


Factor by Grouping

How do factor polynomials with four terms???


factor the expression

Because BOTH expressions have (x+5) – we can use it as the “GCF” and factor it out!

Move the “alike” group to the front, and squish the other terms together!

**Don’t forget the sign**


You try!


Buuuuut... What if the "GCF"

hasn't been factored yet?


Grouping

  • Group the terms.

  • Factor the GCF from each group.

  • Factor out the common binomial.

Reminder: ALWAYS check for a GCF first!!!


Factor by Grouping


Factor by Grouping


Factor by Grouping


You Try!!!


Factoring x2+ bx + c

To FACTOR a trinomial means to write it as the product of two binomials.

Factor x2+6x + 8

What two numbers multiply to give you 8, but add to give you 6?

x2+6x + 8

x2+2x +4x + 8


Ex: 2

Factor x2+3x + 2

(x + 2) (x + 1)

What two numbers multiply to give you the last number…

and add to give you the middle number?


Ex: 3

Factor x2-3x + 2

(x - 2) (x - 1)

What two numbers multiply to give you the last number…

and add to give you the middle number?


Ex: 4

Factor x2-2x - 8

(x - 4) (x + 2)


Ex: 5

Factor x2 - 5x - 14

(x - 7) (x + 2)


Ex: 6

Factor x2 - 16x + 64

(x - 8) (x - 8)

Same thing as (x - 8)2


TRY THESE!

Factor:

  • x2 + 7x + 6

  • x2 – 5x - 24

  • x2 + 10x + 24


Homework:p. 95(13-24)p. 83(1-9)**Your Answers Will NOT Match the Answers in the Back of the Book.


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