Question

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

Answer 1

Answer :

Remainder = 5a

Note :

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

★ Factor theorem :

If the remainder obtained on dividing a polynomial p(x) by (x - c) is zero ,

ie. if R = p(c) = 0 , then (x - c) is a factor of the polynomial p(x) .

If (x - c) is a factor of the polynomial p(x) , then the remainder obtained on dividing the polynomial p(x) by (x - c) is zero ,

ie. R = p(c) = 0 .

Solution :

Here ,

The given polynomial is ;

x³ - ax² + 6x - a .

Let the given polynomial is p(x) ,

Thus ,

p(x) = x³ - ax² + 6x - a

We need to find the remainder obtained when p(x) is divided by (x - a) .

Thus ,

If x - a = 0 , then x = a

Now ,

The remainder will be given as ;

=> R = p(a)

=> R = a³ - a•a² + 6a - a

=> R = a³ - a³ + 5a

=> R = 5a

Hence ,

Remainder = 5a

Answer 2

Answer:

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