Chapter A.3, Problem 72AYU

To determine

To find: The quotient and remainder.

Answer to Problem 72AYU

The quotient is $x^2+ax+a^2$ and remainder is $0$.

Explanation of Solution

Given:

$x^5-a^5$ divided by $x-a$.

Calculation:

$(\text{Quotient})(\text{Divisor})+\text{Remainder}=(x^4+a{x}^3+a^2{x}^2+a^{3}x+a^4)(x-a)+(0)$

$=x^5+a{x}^4+a^2{x}^3+a^3{x}^2+a^{4}x-a{x}^4-a^2{x}^3-a^3{x}^2-a^{4}x-a^5$

$=x^5-a^5=\text{Dividend}$