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 $g(x)=5x^2$
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