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 $g(x)$?

(N/A) According to the division algorithm for polynomials,$p(x) = g(x) \cdot q(x) + r(x)$,where $q(x)$ is the quotient and $r(x)$ is the remainder.
Given that the quotient $q(x) = 0$,the equation becomes $p(x) = g(x) \cdot 0 + r(x)$,which simplifies to $p(x) = r(x)$.
In polynomial division,the degree of the remainder $r(x)$ must be strictly less than the degree of the divisor $g(x)$,i.e.,$\text{deg}(r(x)) < \text{deg}(g(x))$.
Since $p(x) = r(x)$,it follows that $\text{deg}(p(x)) < \text{deg}(g(x))$.
Therefore,the degree of $p(x)$ is less than the degree of $g(x)$.