Question

What is the remainder when $x^4+1$ is divided by $(x-2)$?

• A. $17$
• B. $15$
• C. $7$
• D. $1$

Answer 1

The correct option is A

$17$

Solution:

Given data: The polynomial is $p\left(x\right)=x^4+1$, and it is divided by $(x-2)$.

Finding the remainder:

According to remainder theorem, the remainder will be equal to $p\left(2\right)$ , when $x^4+1$ is divided by $(x-2)$.

$$\begin{gathered} p\left(2\right)=2^4+1 \\ \Rightarrow p\left(2\right)=16+1 \\ \Rightarrow p\left(2\right)=17 \end{gathered}$$

Note: Remainder theorem: If $p\left(x\right)$ is divided by $(x-a)$, then the remainder is equal to $p\left(a\right)$.

Final answer: Hence, the correct answer is option (A).