Question

When $(x^5+1)$ is divided by $(x-2)$, the remainder is:

• A. $5$
• B. $17$
• C. $31$
• D. $33$

Answer 1

Answer: (D)

$33$

The remainder theorem says that when $f\left(x\right)$ is divided by $(x-a)$, the remainder is given by $f\left(a\right)$.

Here, $f\left(x\right)=x^5+1$ and it is divided by $(x-2)$

Since $a=2$

$\therefore Remainder=f\left(2\right)$

$=2^5+1$

$=33$