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 $g(x)$?

(N/A) If a non-zero polynomial $p(x)$ is divided by a polynomial $g(x)$ and the remainder is zero,it implies that $g(x)$ is a factor of $p(x)$. According to the division algorithm for polynomials,$p(x) = g(x) \cdot q(x) + r(x)$,where $r(x) = 0$. Since $p(x)$ and $g(x)$ are non-zero polynomials,the degree of the product $g(x) \cdot q(x)$ must equal the degree of $p(x)$. Therefore,the degree of $g(x)$ must be less than or equal to the degree of $p(x)$,i.e.,$\text{deg}(g(x)) \le \text{deg}(p(x))$.