Question

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

Answer 1

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

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

Put, $x+\pi =0$

$\therefore$ $x=-\pi$

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

Putting $x=-\pi$

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

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

Thus, reminder of $p(-\pi )=-{\pi }^3+3{\pi }^2-3\pi +1$.

$\therefore$ We will get reminder as $-{\pi }^3+3{\pi }^2-3\pi +1$ when $x^3+3x^2+3x+1$ is divided by $x+\pi$.