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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

Warm UP!

EQ: What are ways we can factor polynomials?


Factor the GCF

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




What is the greatest common factor
What is the greatest common factor??

36

24

The number 12






Always look for a Greatest Common Factor 1st.

Factor 4x + 6y

What is their greatest common factor?

= 2( )

2x

+ 3y


3y 8xy

Factor

3y – 8xy

What is their GCF?

= y( )

– 8x

3

2a3 – 6ab2

= 2a( )

a2

– 3b2


2h 2 k 2k

Factor

2h2k + 2k

What is their GCF?

= 2k( )

+ 1

h2

6uv + 9v2

= 3v( )

2u

+ 3v


4x 3 20x 2 24x

Factor

4x3 + 20x2 + 24x

What is their GCF?

= 4x( )

+ 5x

+ 6

x2


6x 3 21x 2 9x

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**



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!!!






Factoring x 2 bx c
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
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
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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