Question

If on division of a non-zero polynomial $p\left(x\right)$ by a polynomial $g\left(x\right)$, the remainder 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 remainder of $p\left(x\right)$ divided by $q\left(x\right)$ is zero, then it might be only possible if $p\left(x\right)\ge g\left(x\right)$ because only then $p\left(x\right)$ will be a multiple of $g\left(x\right)$and won't leave a remainder.

Hence, the degree of $p\left(x\right)$ must be greater than or equal to the degree of $g\left(x\right)$.