Question

Rozłóż wielomian w na czynniki:

w(x)=( -3x+2) ( -2x-3)

Answer 1

w(x)=(x^2 -3x+2) (x^2 -2x-3)

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

 

x^2 to x do potęgi 2

 

x^2 - 3x + 2 = 0

delta1 = b^2 - 4ac

delta1 = (-3)^2 - 4 * 1 * 2

delta1 = 9 - 8

delta1 = 1

x1 = ( -b - pierwiastek z delty ) : 2a

x1 = ( 3 - 1 ) : 2

x1 =  1

x2 = ( -b + pierwiastek z delty ) : 2a

x2 = ( 3 + 1 ) : 2

x2 = 2

 

czyli z pierwszego nawiasu wychodzi:

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

 

 

x^2 - 2x - 3 = 0

delta2 = b^2 - 4ac

delta2 = (-2)^2 - 4 * 1 * (-3)

delta2 =  4 + 12

delta2 = 16

pierwiastek z delty 2 = 4

x1 = ( -b - pierwiastek z delty ) : 2a

x1 = ( 2 - 4 ) : 2

x1 = -2 : 2

x1 = - 1

x2 = ( -b + pierwiastek z delty ) : 2a

x2 = ( 2 + 4 ) : 2

x2 = 6 : 2

x2 = 3

 

czyli z drugiego nawiasu wychodzi :

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

 

 

Answer 2

w(x) = ( x^2 - 3x + 2)( x^2 - 2x - 3) =

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

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lub

delta 1 = (-3)^2 - 4*1*2 = 9 - 8 = 1

x1 = [ 3 - 1]/2 = 1

x2 = [ 3 + 1]/2 = 2

czyli

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

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delta 2 = (-2)^2 -4*1*(-3) = 4 + 12 = 16

p(delty 2) = 4

x3 = [2 - 4]/2 = -2/2 = - 1

x4 = [ 2 + 4]/2 = 6/2 = 3

czyli

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

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więc

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

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