CBSE Class 10 Answered

Suppose that you are workingon p(x) being divided by g(x) giving quotient q(x) and remainder r(x)

(i) when deg p(x)=deg q(x),

e.g when you divide a  quadratic polynomial with a  polynomial of degree zero i.e. a constant term, you will get the degree of the quotient as two , .So the condition you want is achieved.

The same can be achieved by dividing any polynomial with a polynomial of degree zero.

(ii) When you divide say a cubic poly with a quadratic , quotien will be of degree 1 and you may be able to get a remainder of degree 1 , too..

(iii)  When you divide a polynomial by another polynomial of lesser degree, then you may be able to get a remainder which is a real number, which means the degree of the remainder is zero.