Answer
quotient $=x^4+ax^3+a^2x^2+a^3x+a^4$,
remainder$=0$
Work Step by Step
1. Use the factor rule $\:x^n+y^n=\left(x+y\right)\left(x^{n-1}-x^{n-2}y+\dots -xy^{n-2}+y^{n-1}\right)$,
we have $x^5-a^5=(x-a)(x^4+ax^3+a^2x^2+a^3x+a^4)$,
thus for $x^5-a^5$ divided by $x-a$, we get:
quotient $=x^4+ax^3+a^2x^2+a^3x+a^4$,
remainder$=0$
2. To verify, we have $(x^4+ax^3+a^2x^2+a^3x+a^4)(x-a)+(0)=x^5-a^5$
