Question

What is the degree of the zero polynomial?

Answer 1

Define the degree of the zero polynomial.

We know that the general polynomial $p\left(x\right)$ of $n$-th degree can be written as follows:
$p\left(x\right)=a_0+a_{1}x+a_2{x}^2+a_3{x}^3+......+a_n{x}^3$, where $a_i^{\text{'}}s$ are constants and $a_n\ne 0$.

So, zero polynomial is written as:

$0=0+0x+0x^2+0x^3+............+0x^n.$

Therefore, the highest power of $x$ is zero in a zero polynomial, which implies that its degree is also $0$.

Hence, the degree of a zero polynomial is $0$.