Question

Divide $x^3+1$ by $x+1$, find the quotient and the remainder.

Answer 1

We have $x^3+1=(x+1)(x^2-x+1)$.

Now, $\frac{x^3+1}{(x+1)}=\frac{(x+1)(x^2-x+1)}{x+1}=(x^2-x+1)$.

So when $x^3+1$ is divided by $(x+1)$ then the quotient be $x^2-x+1$ and the remainder will be $0$ [ Since $x^3+1$ is perfectly divisible by $(x+1)$]..