Find the remainder when x³ - ax² + 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) = x³ - ax² + 6x - a

The root of x - a = 0 is a.

p(a) = (a)³ - a(a)² + 6(a) - a

= a³ - a³ + 5a

= 5a

Hence by remainder theorem, 5a is the remainder when x³ - ax² + 6x - a is divided by x - a.

☛ Check: NCERT Solutions Class 9 Maths Chapter 2

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 x³ - ax² + 6x - a is divided by x - a is 5a.

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