Find the remainder when `p(x)=x^3-a x^2+6x-a` is divided by `(x-a)dot`

Explanation

Let `p(x)` be any polynomial of degree greater than or equal to one and let `a` be any real number. If a polynomial `p(x)` is divided by `x - a` then the remainder is `p(a)`.
Let `p(x) = x^3 - ax^2 + 6x - a`
The root of `x - a = 0` is `a`.
`p(a) = (a)^3 - a(a)^2 + 6(a) - a`
`= a^3 - a^3 + 5a`
`= 5a`
Hence by the remainder theorem, `5a` is the remainder when `x^3 - ax^2 + 6x - a` is divided by `x - a`.