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Warm UP!

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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???

ALL ANIMALS

ALL FLY

36

24

The number 12

5a

35

The number 5

3y

-8xy

y

-11x

22x2

11x

-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

What is their GCF?

= y( )

– 8x

3

2a3 – 6ab2

= 2a( )

a2

– 3b2

Factor

What is their GCF?

= 2k( )

+ 1

h2

6uv + 9v2

= 3v( )

2u

+ 3v

Factor

What is their GCF?

= 4x( )

+ 5x

+ 6

x2

Factor

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!!!

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

Factor:

- x2 + 7x + 6
- x2 – 5x - 24
- x2 + 10x + 24