Question

The remainder when x¹⁵ is divided by x + 1 is __________.

Answer 1

Let f(x) = x¹⁵

To find the remainder obtained when x¹⁵ is divided by x + 1,

we use remainder theorem, put x + 1 = 0.

f(−1) is the remainder.

Now,

$$\begin{gathered} f\left(-1\right)={\left(-1\right)}^{15} \\ =-1 \end{gathered}$$

Hence, the remainder when x¹⁵ is divided by x + 1 is −1.