Question

If $x^3+2x+1$is divided by $x-2$, then the remainder is:

• A. 13
• B. 12
• C. 10
• D. None of these

Answer 1

The correct option is A

13

According to the remainder theorem:

When a polynomial $p\left(x\right)$ is divided by $(x-a)$, then the remainder would be $p\left(a\right)$.

Therefore,

The remainder when $p\left(x\right)=x^3+2x+1$is divided by $x-2$ is:

$$\begin{gathered} p\left(2\right)=2^3+2\times 2+1 \\ =8+4+1 \\ =13 \end{gathered}$$

Hence, option A is correct.