Question

Which one of the following statements is correct?

If $x^6+1$ is divided by $x-1$ reminder is $-1$.

• A. True
• B. False

Answer 1

The correct option is B False

Remainder theorem.

If a polynomial $p\left(x\right)$ is divided by a linear polynomial $(x-a)$. Then, the remainder is $p\left(a\right)$.

Let, $p\left(x\right)=x^6+1$, divided by $(x-1)$.

The remainder is computed as,

$$\begin{gathered} p\left(1\right)={\left(1\right)}^6+1 \\ \Rightarrow =1+1 \\ \Rightarrow =2 \end{gathered}$$

Thus, the remainder is $2$.

Hence, the given statement is false.