Chapter 2.4, Problem 60E

Solution

The remainder when $f\left(x\right)=x^{63}-17$ is divided by $x-1$ .

The required remainder is −16.

Given:

  $f\left(x\right)=x^{63}-17$

Concept Used:

Remainder Theorem: when polynomial $f\left(x\right)$ is divided by the polynomial $x-k$ , then $f\left(k\right)$ gives the remainder.

Calculation:

  $\begin{array}{l}f\left(1\right)={\left(1\right)}^{63}-17\\ f\left(1\right)=1-17\\ f\left(1\right)=-16\end{array}$

Therefore, the remainder is −16.