Explicație pas cu pas:
[tex]P(X) = X^{4} - 1 = (X - 1)(X^{3} + X^{2} + X + 1) = \\ [/tex]
[tex]= (X - 1)(X^{3} + X^{2} + X) + (X - 1) \\ [/tex]
[tex]= X(X - 1)(X^{2} + X + 1) + X - 1[/tex]
=>
[tex]P(X) : Q(X) = {X}^{2} - X , \ rest \ X - 1 \\ [/tex]
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Explicație pas cu pas:
[tex]P(X) = X^{4} - 1 = (X - 1)(X^{3} + X^{2} + X + 1) = \\ [/tex]
[tex]= (X - 1)(X^{3} + X^{2} + X) + (X - 1) \\ [/tex]
[tex]= X(X - 1)(X^{2} + X + 1) + X - 1[/tex]
=>
[tex]P(X) : Q(X) = {X}^{2} - X , \ rest \ X - 1 \\ [/tex]