(X^3+1)dividend (x-1)

Question

asked Aug 1, 2020 131k views

1 Answer

Chindit · Answer 1 · 2020-08-05T10:00:26+0000

$x^3=x\cdot x^2$ and
x^2(x-1)=x^3-x^2 . So we have a remainder of

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

$x^2=x\cdot x$ and
x(x-1)=x^2-x . Subtracting this from the previous remainder gives a new remainder

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

$x=x\cdot1$ and
1(x-1)=x-1 . Subtracting this from the previous remainder gives a new one of

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

and we're done since 2 does not divide
. So we have

$(x^3+1)/(x-1)=x^2+x+1+\frac2{x-1}$