Question

Find the remainder when $x^3+1$ divided by $(x+1)$.

Answer 1

Given, polynomial $x^3+1$ divided by $(x+1)$.

Then, $f\left(x\right)=x^3+1$.

The polynomial is divided by $(x+1)$ .

Then put$(x+1)=0⟹$ $x=-1$, we get,

$f(-1)=(-1{)}^3+1$

$\Rightarrow f(-1)=-1+1$

$\Rightarrow f(-1)=0$.

So, when $f\left(x\right)=x^3+1$ is divided by $x+1$, the remainder obtained is zero.

So, by Remainder Theorem, we know that $f\left(x\right)=x^3+1$ when divided by $x+1$, gives $0$ as the remainder.