Rozłóż na czynniki wielomiany metodą grupowania wyrazów.W(x)=x^6-x^5-x^2+x=
W(x)=x^6-x^5-x^2+x= x^5( x- 1 ) - x( x -1 ) = ( x -1 )( x^5 - x ) = ( x - 1 )( x^4 - 1 )x = x(x-1)(x^4 - 1^4 ) = x( x -1 )( x^2 - 1 )( x^2 + 1 ) = x(x-1)(x-1)(x+1)(x^2+1)
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W(x)=x^6-x^5-x^2+x= x^5( x- 1 ) - x( x -1 ) = ( x -1 )( x^5 - x ) = ( x - 1 )( x^4 - 1 )x = x(x-1)(x^4 - 1^4 ) = x( x -1 )( x^2 - 1 )( x^2 + 1 ) = x(x-1)(x-1)(x+1)(x^2+1)