# 5.1 Multiplying Polynomials - Mr. Sjokvist ... 5.1 Multiplying Polynomials Recall Adding Polynomials: (2g+3b) + (1g+2b) =3g+5b What happens with (2g+3b) * (1g+2b)? Nov 1 10:22 AM x

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### Text of 5.1 Multiplying Polynomials - Mr. Sjokvist ... 5.1 Multiplying Polynomials Recall Adding...

• 1

Nov 1­5:03 PM

5.1 Multiplying Polynomials

(2g+3b) + (1g+2b) =3g+5b

What happens with (2g+3b) * (1g+2b)?

Nov 1­10:22 AM

x

1

x

x x2 x2

x x

A=l*w =2x(x+1)=2x^2+2x

Nov 1­10:22 AM

x

1

x x 2

x

­x

­x­1

­x

(2x-2)(x-1) =2x^2-2x-2x+2 2x^2-4x+2 Success!!!

x

x2

11

­1 ­1

­x

­x ­x

x2

Nov 1­10:22 AM

x

1

x

x2

x2

xx

1 1

x x

1 1

­x

­1 ­1

­x2 ­x2

­1 ­1

Nov 1­10:48 AM Nov 2­8:41 AM

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Nov 2­2:18 PM

2x^2-8xy-xy+4y^2 F O I L 2x2-9xy+4y2

Nov 2­9:53 AM

Test Rewrite options: -redo just one section -redo just one learning outcome -redo whole test?!

Before the retest: -finish review -do corrections -tomorrow lunch tutorial

Nov 1­5:03 PM

5.2 Common Factors x

1

x

x x2 x2

x x

Nov 1­5:11 PM

Nov 1­5:11 PM Nov 2­9:22 AM

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Nov 8­9:45 AM

Cam Jillian

66 23716

2x3x11 2x2x7x7x11x11

2x2x3x7x7x11x11=71148

Nov 8­2:24 PM

Find the "All-Star" "Dream Team" please-everyone, Mountain High, Super Hero Pizza

1: Crust 2: Cheese 3: Pepperoni 5: Pineapple 7: Mushrooms x: "mystery" meat y: "mega mouthwatering mystery" meat

Jasmine: 63x2 Nick: 12xy Gregory: 18x

Nov 2­9:33 AM Nov 2­2:09 PM

Nov 2­9:38 AM Nov 2­9:52 AM

p. 220 #(1-7, 12)o.l.

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Nov 2­2:33 PM

§ 5.3 Factoring Trinomials

x2 x2

x x

x x

11

To factor this expression, set up algebra tiles that give a product of 2x2+4x+2

2x2+4x+2=(x+1)(2x+2)

x

x x 1 1

1

Nov 2­2:37 PM

x

1

x

xx 2

x x

1 1

x x

11

Ex 2: set up tiles for x2+7x+10

xxxx

11111 1

Nov 2­2:37 PM

x

1

x

x x2

x x

1 1

x x

11

Ex 2: set up tiles for x2+7x+10

xxxx

11111 1

1 1

11111

x2+7x+10=(x+5)(x+2)

Nov 2­2:37 PM

x

1

x

x x2

x x

1 1

x

x

11

Ex 2: set up tiles for 2x2+3x+1

x

x

x x

11111 1

1

1 1

1111

x2+7x+10=(x+5)(x+2)

x2

2x2+3x+1=(x+1)(2x+1)

Nov 2­2:37 PM

x 1x

x x2

x x

1 1

x

x

11

Ex 2b: set up tiles for 3x2+5x-2

x

x

x x

11111 1

1 1 1

1111

x2+7x+10=(x+5)(x+2)

x2

­x

­1

­1

x2

x

x

x

x x ­1

Nov 3­2:17 PM

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Nov 3­3:03 PM Nov 3­9:07 AM

Can we do this without algebra tiles?

Ex 1: x2+3x+2=(x+_)(x+_)

Our missing numbers should be integers with a sum of 3 and a product of 2

x2+3x+2=(x+1)(x+2)

Integers Sum Product

­1,­2 ­3 2

1,2 3 2

­1,4 3 ­4

1,­2 ­1 ­2

1,3 4 3

Nov 2­2:37 PM

Start p. 235: #1-4

Nov 3­9:07 AM

Ex 2: x2+3x­4=(x+_)(x­_)

Our missing numbers should be integers with a sum of 3 and a product of -4

x2+3x­4=(x+4)(x­1)

Integers Sum Product

­1,­2 ­3 2

1,2 3 2

­1,4 3 ­4

1,­2 ­1 ­2

1,3 4 3

Nov 3­9:07 AM

Ex 3: 2x2+6x­8

If all three terms have a common factor, we can deal with this first!

x2+3x­4=(x+4)(x­1)

Ex 3: 2x2+6x­8=2(x2+3x­4)

Nov 5­10:39 AM

The difficult ones:

Ex: factor 2x2+11x+12

try splitting up the middle term to get two binomials that factor nicely :)

2x2+8x+3x+12 2x(x+4)+3(x+4) (2x+3)(x+4)

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Nov 5­10:39 AM

How do you know?

Ex: factor 2x2+11x+12 -look for two integers with a sum of 11 and a product of 24!

2x2+8x+3x+12 2x(x+4)+3(x+4) (2x+3)(x+4)

Mar 10­11:12 AM

Mar 10­11:14 AM Nov 5­10:39 AM

Method 3

We know (x+a)(x+b) "foils" to give us x2+(a+b)x+ab So why not try skipping straight to

(x+_)(x+_) when factoring?

Ex: factor x2+5x+6

try writing (x+ )(x+ ) now fill in the blanks with an educated guess!

Nov 15­8:56 AM Nov 15­2:06 PM

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Nov 15­9:04 AM Nov 2­2:37 PM

Finish p. 235 #1-4, continue #(5-9) o.l.

Nov 4­10:14 AM

"Perfect" Trinomials

ex 1) x2-4=x2+0x-4

perfect squares

A difference of squares always factors like: (x+2)(x-2)

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Nov 4­10:44 AM Nov 4­10:48 AM

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Nov 4­10:50 AM Nov 15­2:10 PM

Nov 2­2:40 PM

p. 246 #(1-7) o.l., 14

Nov 2­2:40 PM

Review: p. 252 #1-2, 6-7, 10-11, 13-15

Oct 3­3:05 PM

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