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

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.