2. Find the remainder when \(x^3 - ax^2 + 6x - a\) is divided by x - a.

Let \(p(x) = x^3 - ax^2 + 6x - a\)

The zero of \(x - a\) is x = a i.e. (x - a = 0)

So, \(p(a) = {a}^3 - a{a}^2 + 6{a} - a\)

i.e. \(p(a) = a^3 - a^3 + 6a - a\)

i.e.\(p(a) = 5a\)

Hence, By remainder theorem, required remainder = 5a.