Q.2. Find the remainder when x3 - ax2 + 6x - a is divided by x - a.

Solution:

The remainder can be obtained by either long division method or by remainder theorem.

Using the remainder theorem,

p(x) = x3 - ax2 + 6x - a

g(x) = x - a

Put g(x) = 0, i.e., x - a = 0 ⇒ x = a

Now, p(a) = a3 - a × a2 + 6 × a - a

= a3 - a3 + 6a - a = 5a

Therefore, remainder will be 5a