**Q.2.** Find the remainder when *x*^{3} - *ax*^{2} + 6*x* - *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*) = *x*^{3} - *ax*^{2} + 6*x* - *a*

*g*(*x*) = *x* - *a*

Put *g*(*x*) = 0, i.e., *x* - *a *= 0 ⇒ *x* = *a*

Now, *p*(*a*) = *a*^{3} - *a *× *a*^{2} + 6 × *a* - *a*

= *a*^{3} - *a*^{3} + 6*a* - *a* = 5*a*

Therefore, remainder will be 5*a*