Question

The remainder obtained when the polynomial $x^{64}+x^{27}+1$ is divided by $\left(x+1\right)$ is

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

The correct option is A

$1$

Find the remainder

Remainder theorem states that if a polynomial $p\left(x\right)$ is divided by the binomial $\left(x-a\right)$ then the remainder can be determined by finding $f\left(a\right)$

Here $p\left(x\right)=x^{64}+x^{27}+1$ and $a=-1$

$$\begin{gathered} p\left(-1\right)={\left(-1\right)}^{64}+{\left(-1\right)}^{27}+1 \\ =1-1+1 \\ =1 \end{gathered}$$

Therefore, the remainder is $1$

Hence, the correct option is $\left(\mathrm{A}\right)$