Question

If on division of a polynomial $p\left(x\right)$ by a polynomial $g\left(x\right)$, the quotient is zero, what is the relation between the degrees of $p\left(x\right)$ and $g\left(x\right)$?

Answer 1

Solve for the relation between $p\left(x\right)$ and $g\left(x\right)$

Since, the quotient of $p\left(x\right)$ divided by $g\left(x\right)$ is zero.

Then it might be only possible if degree of $p\left(x\right)<g\left(x\right)$.

Hence, the degree of $p\left(x\right)$ is smaller than the degree of $g\left(x\right)$.