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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

    Recall Adding 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

  • 2

    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

  • 3

    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.

  • 4

    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

  • 5

    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)

  • 6

    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

  • 7

    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)

    Mar 14­9:08 AM

    Nov 4­10:44 AM Nov 4­10:48 AM

  • 8

    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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