# Find the remainder when x^{3} - ax^{2} + 6x - a is divided by x - a.

**Solution:**

Let p(x) be any polynomial of degree greater than or equal to one and let 'a' be any real number. If a polynomial p(x) is divided by x - a then the remainder is p(a).

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

The root of x - a = 0 is a.

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

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

= 5a

Hence by remainder theorem, 5a is the remainder when x^{3} - ax^{2} + 6x - a is divided by x - a.

**Video Solution:**

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

### NCERT Solutions Class 9 Maths - Chapter 2 Exercise 2.3 Question 2:

**Summary:**

The remainder when x^{3} - ax^{2} + 6x - a is divided by x - a is 5a.