Question

Find the remainder when $x^3+3x^2+3x+1$ is divided by $x+\mathrm{\pi }$.

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 $x+\mathrm{\pi }$.

Put divisor $x+\mathrm{\pi }$$=0$

$\Rightarrow$ $x=-\mathrm{\pi }$

Step $2$: Determine the Remainder

Consider the equation

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

By remainder theorem,

Putting $x=-\mathrm{\pi }$

$\therefore$Remainder is

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

$=-{\mathrm{\pi }}^3+3{\mathrm{\pi }}^2-3\mathrm{\pi }+1$

Hence, remainder when $x^3+3x^2+3x+1$ is divided by $x+\mathrm{\pi }$ is $-{\mathrm{\pi }}^3+3{\mathrm{\pi }}^2-3\mathrm{\pi }+1$.