Question

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

Answer 1

Step 1: Determine the value of $x$ for the divisor

Given equation is $x^3+3x^2+3x+1$ which is divided by $x+1$.

Put divisor $x+1$$=0$

$\Rightarrow$ $x=-1$

Step 2: Determine the Remainder

Consider the equation

$x^3+3x^2+3x+1$

By remainder theorem,

Putting $x=-1$

$\therefore$Remainder is

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

$=-1+3-3+1$

$=0$

Hence, remainder when $x^3+3x^2+3x+1$ is divided by $x+1$ is $0$.