8-1 - 49 1) 1, 36 2, 18-4, -9-1-2-5 2) −10x y2 10x y2 5x y2 2x y2 10 2 −2xy, 5x 10 ......

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Transcript of 8-1 - 49 1) 1, 36 2, 18-4, -9-1-2-5 2) −10x y2 10x y2 5x y2 2x y2 10 2 −2xy, 5x 10 ......

  • Objective- To find factors of numerical and variable expressions.

    Factor - A whole number or variable expressionthat divides evenly into a given wholenumber or variable expression.

    List all the positive factors of the following.

    18 24 5xy1 182 93 6

    1 242 123 84 6

    1 5xy5 xy5x y5y x

    FactorTower

    Find three factorizations for each monomial.

    361 362 183 124 9

    1) 1, 362, 18

    -4, -9

    -1-2-5

    2) 210x y210x y

    25x y22x y

    10 22xy, 5x

    210

    22, 5x y

    6 6-1 -36-2 -18-3 -12-4 -9-6 -6

    -10 2x y-1x-2x-5x

    10xy5xy2xy

    -10x xy......

    210y, x

    Composite - Made up of distinct parts- WebstersComposite Number - Numbers that are made up

    of a product of primes.Prime Factorization - The unique set of prime

    numbers whose productequals a given number.

    W it th i f t i ti f th f ll iWrite the prime factorization for the following.18 24 5xy

    FactorTree 2 9

    3 3

    4 6

    2 32 2

    5 xy

    x y

    2 32 23 3 5 x y

    Find the prime factorization of the given number.Factor Tree Upside-Down Division

    840 840

    2 420

    2 210

    2420221021055

    2

    3 7

    105

    5 21

    2173

    32 3 5 7

    32 3 5 7

    Largestnumber that divides evenly into a given setof numbers.

    GCF - Greatest Common Factor -

    Greatest Common Factor

    Two ways to find the GCF1) Make a list of factors.

    2) Select common factors from the primefactorizations.

    Find the GCF using the technique described.

    Make a List Prime Factorization60

    1 602 303 20

    841 842 423 28

    60

    2 30

    2 15

    84

    2 42

    2 213 204 155 126 10

    3 284 216 147 12

    GCF = 12

    2 15

    3 5

    2 21

    3 7

    2 2 3 5 2 2 3 7 GCF 2 2 3=

    GCF = 12

    Lesson 8-1

    Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk 2010

  • GCF - Greatest Common Factor

    Find the GCF of the following.

    20 24

    2 10 2 12

    2 5

    2 2 5

    2 6

    2 32 2 2 3

    GCF = 2 2 = 4

    GCF - Greatest Common Factor

    Find the GCF of the following.

    9mn

    6 9 mn6m2

    m2

    2 3mm 3 3mn

    GCF = 3m = 3m

    m m2 3 m n3 3

    Finding the GCF Using Upside-Down Division

    200 1802100 90250 45510 925

    33

    Common Factors

    5 3

    GCF 2 2 5=

    GCF = 20

    Find the GCF using the technique described.Factor Trees Upside-Down Division

    96

    2 48

    6 8

    240

    2 120

    4 30

    2 3 2 4 2 2 2 15

    96 240248 120224 60212 3026 153

    2 2 2 2 2 3 2 2 2 2 3 5

    GCF 2 2 2 2 3= GCF = 48

    2 3 2 4

    2 2

    2 2 2 15

    3 5GCF 2 2 2 2 3=

    GCF = 48

    6 1532 5

    GCF - Greatest Common Factor

    Find the GCF of the following mentally.

    1) 15x2y 12xy3 3x y

    2)

    3)

    30a2b 42a3b2

    14m4n3 21m5n2

    6 2a b

    7 4m 2n

    Find the missing factor.

    1)

    2)

    3)

    x10 = (x4 )( )

    8a4 = (2a)( )

    2x2y = (x)( )

    6x

    34a

    2xy

    4)

    5)

    6)

    36a3b4 = (9ab)( )

    7x4 y3 = (xy2)( )

    6h2k3 = (3hk)( )

    2 34a b37x y

    22hk

    Lesson 8-1 (cont.)

    Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk 2010

  • GCF Word ProblemsA baker has 16 loaves of white bread and 40 loaves of wheat. He wants to store the loaves with the samenumber of loaves on each shelf, while keeping whiteand wheat on separate shelves. If he puts the greatest possible number of loaves on each shelf, how many shelves will he need?

    White = 16 loaves Wheat = 40 loavesGCF = 8

    Shelves Needed for White =Shelves Needed for Wheat =

    Total Shelves Needed =

    16 8 2 shelves=40 8 5 shelves=

    7 shelves

    Lesson 8-1 (cont.)

    Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk 2010