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15 July, 12:09

Factorise 45x^2 - 46x + 8

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  1. 15 July, 14:16
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    The way to do this is if the equtation is in

    ax^2+bx+c form

    then multiply a and c together and get

    a times c=y times z where y+z=b then make the form into

    ax^2+yx+zx+c so

    a=45

    b=-46

    c=8

    a time c=45 times 8=360

    then find what 2 numbers add up to - 48 and multiply to get 360

    the numbers must be both negative because only same signs multiplied by each other can result in a positive number

    factor 360

    360,1

    180,2

    120,3

    90,4

    72,5

    60,6

    45,8

    40,9

    36,10

    30,12

    24,15

    20,18

    now add and find which add up to 48

    360+1=361

    180+2=182

    120+3=123

    90+4=94

    72+5=77

    60+6=66

    45+8=53

    40+9=49

    36+10=46 match

    30+12=42

    24+15=39

    20+18=38

    the numbers are - 36 and - 10

    split it up

    45x^2-10x-36x+8

    group

    (45x^2-10x) + (-36x+8)

    factor out the common factors

    (5x) (9x-2) + (-4) (9x-2)

    reverse distributive property which is ab+ac=a (b+c)

    (5x-4) (9x-2)

    tada, it's factored

    factored form is (5x-4) (9x-2)
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