Question

rozłoż wielomiany na czynniki a)x^3-4x+3

Answer 1

x^3 - 4x + 3 = x^3 - x - 3x + 3 = x*(x^2 - 1) - 3*(x - 1) =

= x*(x-1)*(x + 1) - 3 *(x -1) = (x -1)[ x*(x +1) - 3] =

= (x -1)*( x^2 + x - 3)

  delta = 1^2 - 4*1*(-3) = 1 + 12 = 13

p(delty) = p(13)

x1 = [ -1 - p(13)] /2

x 2= [ - 1 + p(13)]/2

zatem

 

x^2 + x - 3 = [ x + (1 + p(13))/2]*[ x - ( - 1 + p(13)/2 ]

oraz

x^3 - 4x + 3 = (x - 1)*[ x +( 1 +p(13))/2]*[ x - ( - 1 +p(13))/2) ]

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