Question 195047
4x +8
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if  we  divide  both  terms  by  2,  and  the multiply  both  by  2,  the  expression  stays  the  same.
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  (2) 4x/(2) + (2) 8/(2)
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now  lets  take  out  the  common  factors  of  the  numerator,  2
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(2)  { 4x/2 +8/2 }
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and  now  simplify  each  term
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(2) { 2x +4}
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Normally  we  do  not  do  all of  these  steps,  we  simply  define  the  greatest  common  factor, and  extract  it  from  the  expression,,,being  careful  to  respect  all  of  the  terms.
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For  example:
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  3x3 +6x^2 +9x
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The  greatest  common  number  factor  is  3,  and  the  greatest  common  variable  factor  is  x
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(3x) { 3x^3/3x +6x^2 /3x +9x/3x }
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3x ( x^2 +2x +3)
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we  can  check  the  answer  by  distributing,  
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3x(x^2) = 3x^3  ok,,,3x (2x) = 6x^2  ok,,,3x (3)=9x ok
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one  more  example,  this  time  with  negatives
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5x4 -15x^3 +20x^2 -25x
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greatest  common  number  is  5,  greatest  common  variable  is  x,  therefore  5x
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5x{  5x^4/5x - 15x^3/5x +20x^2 5x -25x/5x }
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simplying
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5x { x^3 - 3x^2 +4 x - 5 }
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checking: 5x(x^3)=5x^4,,ok,,,,5x (-3x^2)= -15x^3,,ok,,,5x(4x)=20x^2,ok,,,,5x( -5) =-25x,  ok.
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just  take  it  step  by  step,  until  it  becomes  second  nature
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Good  Luck,,,,keep  up  hard  work