Answer the following and justify:
If on division of a polynomial $ p(x) $ by a polynomial $ g(x) $, the quotient is zero, what is the relation between the degrees of $ p(x) $ and $ g(x) $ ?

Given:

On division of a polynomial \( p(x) \) by a polynomial \( g(x) \), the quotient is zero.

To do:

We have to find the relation between the degrees of \( p(x) \) and \( g(x) \).

Solution:

If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, then the relation between the degrees of p(x) and g(x) is the degree of p(x) is less than the degree of g(x).

For example,

$p(x)=10x$ and $g(x)=5x^2$