Question

A polynomial whose degree is not defined is .

Answer 1

$\underset{–}{\text{Zero Polynomial:}}$
$\bullet$ We learnt earlier that $f\left(x\right)=a_n{x}^n+a_{n–1}{x}^{n–1}+\dots +a_{1}x+a_{0}f\left(x\right)=anxn+an–1xn–1+\dots +a1x+a0$ is a polynomial.
$\bullet$ Now, a zero polynomial is a special case of the polynomial where all the coefficients $a_n,a_{n–1},a_{n–2},\dots \dots a_1,a_0$ are zeros $\left(0\right).$ Hence, the polynomial becomes $f\left(x\right)=0$ or the corresponding polynomial function is the constant function with value $0.$
$\bullet$ $f\left(x\right)=0,g\left(x\right)=0x,h\left(x\right)=0x^2,p\left(x\right)=0x^3,q\left(x\right)=0x^{12},r\left(x\right)=0x^{50}$
etc. are all examples of zero polynomials.
$\bullet$ As seen in the examples above, the degree of a zero polynomial can be $0,1,2,3,12,50,$ and so on, indicating that the degree of a zero polynomial is not a fixed number. As a result, the degree of a zero polynomial isn't defined.

$\underset{–}{\text{Note:}}$
The zero polynomial is considered as the additive identity of the polynomials.