Question

determine o quociente é o resto da divisão de x ao cubo menos 1 por x menos 1​

Answer 1

x3 - 1 ÷ ( x - 1 )

( x - 1 )• ( x2 + x + 1 ) / ( x - 1 ) [ cancelar ( x - 1 ) com ( x - 1 ) então fica:

quociente: x2 + x + 1

resto: zero

Answer 2

$\left\begin{array}{lll}~~~~x^3-1&~&|\underline{\,~x-1~~~~}\\-&&~x^2\\~~~~x^3-x^2&&\\~~\underline{~~~~~~~~~~~~~~}&&\\~~-1+x^2&&|\underline{\,~x-1~~~~}\\-&&~x^2+x\\~~~~x^2-x&&\\~~\underline{~~~~~~~~~~~~~~}&&\\~~~~x-1&&|\underline{\,~x-1~~~~}\\-&&~x^2+x+1\\~~~~x-1&&\\~~\underline{~~~~~~~~~~~~~~}&&\\~~~~~~\boxed{0}&&\end{array}\right$

Sendo assim, o quociente ficou  x² + x + 1  e o resto ficou  0.