Factoring Trinomials

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Factoring Trinomials
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Warm Up

• Multiply
• 1. (x 3)(x 7)
• 2. (x 6)(x 5)
• 3. (x 2)(x 9)
• 4. (x 4)(x 6)

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Math 2

• Todays Question
• How do I factor trinomials with a leading
  coefficient of one?

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Lets Multiply

• (x2)(x1)
• x2 x 2x 2
• x2 3x 2
• What if we wanted to undo Multiplying?
• Look at the result that we got above
• x2 3x 2
• How can I write this as a product of binomials?
• ( )( )

x
x


2
1
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Ex 1. Factor the TrinomialAlways look for a GCF
First!!

• x2 4x 3
• ( )( )

GCF??... NO!
x

3
1

x
What multiplies to equal x2
What s multiply to equal 3?
x x
3 and 1
continued
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Ex.1) Continued

• (x 3)(x 1)
• How do I know this is right?
• Look at the product of the outer and inner terms.
• Do they add to give you the middle term?
• YES.so you factored it correctly!

3x
3x x 4x ?
x
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Ex.2) Factor the Trinomial
GCF??... NO!
6
x2

• x2 5x 6
• ( )( )
• So, do we use 2 and 3 or 1 and 6?
• Wellwhich ones will add to give you 5?
• 2 and 3!!
• Check!
• 3x 2x 5x ?

2, 3 1, 6
x, x
x

2
3

x
2x
3x
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Ex. 3) Factor the Trinomial
GCF??... NO!

• x2 2x 3
• ( )( )

-3
x2
x
-
3
1

x
-3, 1 -1, 3
x, x
-3x
x
So, do we use -3 and 1 or -1 and 3? Wellwhich
ones will add to give you -2? -3 and 1!!
Check! x -3x -2x ?
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Practice

• Factor the following
• 1. x2 9x 8
• 2. x2 12x 10
• 3. x2 2x 3
• 4. x2 8x 15

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Factoring with GCF

• Always look for a GCF first
• Ex. 4x2 12x 16
• What is the GCF?
• 4(x2 3x 4)
• Can we factor x2 3x 4 more?
• Are there two numbers that multiply to equal -4
  and add to be -3?
• x2 3x 4 factors to (x 4)(x 1)
• Final answer 4(x 4)(x 1)

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Factoring with GCF

• Example 2 6x2 30x 36
• GCF?
• 6
• 6(x2 5x 6)
• Can be x2 5x 6 factored?
• x2 5x 6 can be factored to (x 3)(x 2)
• Answer 6(x 3)(x 2)

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Practice!!
Factor each Polynomial !!!
Dont forget the GCF!

1. 2(x 2) (x 6)
2. 3x(x 5) (x 2)
3. x(x 7) (x 2)
4. 3(x 5) (x 4)
5. 4(x 4) (x 3)
6. 2x(x - 6)(x 4)

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Class work-begin Factoring WS

• Homework-Finish Factoring WS