# 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 $g(x)$ ?

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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 $p(x) \div g(x)=10x^2 \div 5x^2=2$
Updated on 10-Oct-2022 13:27:09