Question

Wyznacz resztę z dzielenia wielomiany w przez wielomian p b) w(x)=x^10-1, p(x)=x-x^2

Answer 1

W(x) = x¹⁰ - 1   P(x) =  - x² = x( 1 - x)

                                          x (1 - x) = 0

                                          x = 0   ∨ x = 1

W ( 0) = R(0)

W ( 1) = R(1)

 

W(0) = 0¹⁰ - 1 = - 1

W(1) = 1¹⁰ - 1 = 1 - 1 = 0

 

R(x) = ax + b

 

R(0) = a ·0 + b = b

R(1) = a ·1 + b = a + b

 

 b = - 1

a + b = 0

 

a - 1 = 0

a = 1

 

R (x) = x - 1