Question

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

• A. $\pi$
• B. $-{\pi }^2+3{\pi }^3-3\pi +1$
• C. $-{\pi }^3+3{\pi }^2-3\pi +1$
• D. None of these

Answer 1

Answer: (C)

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

The remainder theorem states that when a polynomial, $f\left(x\right)$ is divided by a linear polynomial $(x-a)$, then the remainder of that division will be equivalent to $f\left(a\right)$.

Given:$f\left(x\right)=x^3+3x^2+3x+1$

Here, $f\left(x\right)$ is divided by a linear polynomial $(x+\pi )$, then the remainder of the division will be equivalent to $f(-\pi )$.

Then, remainder $=f(-\pi )={(-\pi )}^3+3{(-\pi )}^2+3(-\pi )+1=-{\pi }^3+3{\pi }^2-3\pi +1$.

Therefore, option $C$ is correct.