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

Given:

On division of a non-zero polynomial \( p(x) \) by a polynomial \( g(x) \), the remainder 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 non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, then g(x) is a factor of p(x) and has a degree less than or equal to the degree of p(x).

For example,

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

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