Question

Find the remainder when $x^3+1$ is dividend by $x+1$.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

Remainder Theorem states that the remainder of the division of a polynomial $f\left(x\right)$ by a linear polynomial $(x-a)$ is $f\left(a\right)$ or in other words $(x-a)$ is divisor of $f\left(x\right)$ if and only if $f\left(a\right)=0$

Here $a=-1$

Remainder is $p(-1)$

$\Rightarrow P(-1)=0$

Hence remainder is $0$