Question

if on division of nonzero polynomial p (x)by a polynomial g (x) the remainder is zero what is relation between the degrees of p (x) and g (x)

Answer 1

Here p(x) denotes the non-zero polynomial, and g(x) is another polynomial which is dividing p(x). We have given that the remainder is 0.

This implies the degree of p(x) is greater than the degree of g(x), because if both have the same degree then the remainder will a non-zero constant.

Therefore, the quotients and dividend, that is, g(x) will be the real factors of p(x).

Answer 2

PX degree will be greater then the degree of GX as if they have the same degree the remainder will be a non zero constant.

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