Question

rozłóż wielomian na czynniki za pomocą grupowania:

a)x^3 - 7x + 6

b)x^3-3x+2

Answer 1

a)   x^3 - 7 x + 6 = x^3 - 6 x - x + 6 = x*( x^2 - 1) - 6*( x - 1) =

= x*( x + 1)*(x -1) - 6*(x - 1) = ( x - 1)*( x*( x + 1) - 6) = ( x -1)*(x^2 + x - 6) =

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

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b)

x63 - 3 x + 2 = x^3 - 2 x - x + 2 = x*( x^2 - 1) - 2*( x - 1) =

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

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

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bo

 delta = 2^2 - 4*1*( -2) = 4 + 8 = 12 = 4*3

p( delty) = 2 p(3)

x1 = [ - 2 - 2 p(3)]/2 = - 1 - p(3)

x2 = [ - 2 + 2 p(3)]/2 = - 1 + p(3)

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p(3)  - pierwiastek kwadratowy z 3