Question

When p(x) = x^3 - ax^2 + x is divided by (x -a), the remainder is (a) 0 (b) a (c) 2a (d) 3a

Answer 1

=>x-a=0

=>x=a

=>p(x)=x³-ax²+x

We know that when p(x) is divided by (x-a),the remainder is p(a)

=>p(a)=a³-a(a)²+a

=>a³-a³+a

=>a

Thus,the remainder is a and correct option is b)a.

Answer 2

Given:

• A polynomial is given to us.
• The polynomial is x³-ax²+x.
• It is divided by (x-a).

To Find:

• The remainder .

Answer:

If the polynomial is divided by (x-a) , then we can find the remainder by putting x = a in the polynomial

On putting the Value we have ,

=> p(x) = x³-ax²+x.

=> p(a) = a³- a × a² + x .

=> p(a) = a³ - a³ + a .

=> p(a) = a.

Hence the required answer is a (b)