Applying Remainder Theorem, let us write the remainders, when,

the polynomial x³ – ax² + 2x – a is divided by (x – a)

Remainder theorem says that,

f(x) is a polynomial of degree n (n ≥ 1) and ‘a’ is any real number. If f(x) is divided by (x – a), then the remainder will be f(a).

Let us solve the following questions on the basis of this remainder theorem.

Let f(x) = x³ – ax² + 2x – a …(1)

When x³ – ax² + 2x – a is divided by (x – a).

Now, let’s find out the zero of the linear polynomial, (x – a).

To find zero,

x – a = 0

⇒ x = a

This means that by remainder theorem, when x³ – ax² + 2x – a is divided by (x – a), the remainder comes out to be f(a).

From equation (1), remainder can be calculated as,

Remainder = f(a)

⇒ Remainder = (a)³ – a(a)² + 2(a) – a

⇒ Remainder = a³ – a³ + 2a – a

⇒ Remainder = 2a – a

⇒ Remainder = a

∴ the required remainder = a