Question

Find the remainder when $x^3+3x^2+3x+1$ is divided by
$x+1$

Answer 1

Dividing $x^3+3x^2+3x+1$ by $x+1$

So, $x^3+3x^2+3x+1$ is dividend and $x+1$ is divisor.

Put, $x+1=0$

$\therefore$ $x=-1$

Let $p\left(x\right)=x^3+3x^2+3x+1$

By remainder theorem, $p(-1)$ is the remainder.

Putting $x=-1$

$p(-1)=(-1{)}^3+3(-1{)}^2+3(-1)+1$

$=-1+3-3+1$

$=0$

Thus, reminder of $p(-1)=0$.

$\therefore$ We will get reminder as $0$ when $x^3+3x^2+3x+1$ is divided by $x+1$.