Question

wyznacz reszte z dzielenia wielomianu W(x)=x^1985+1 przez P(x)=x^2-1

Answer 1

W(x)=x¹⁹⁸⁵+1      P(x) = x² - 1 = ( x - 1 ) ( x + 1 )

                                                    

W ( 1 ) = R

W  (- 1) = R 

 

R ( x ) = ax + b

 

W ( 1 ) = 1¹⁹⁸⁵ + 1 = 1 + 1 = 2

W ( -1) =  - 1¹⁹⁸⁵ =  - 1 + 1 = 0

 

a + b = 2

-a + b = 0

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 2b = 2

  b = 1

  a = 2 - 1 = 1

 

R ( x ) = x + 1