∙ We learnt earlier that f(x)=anxn+an–1xn–1+…+a1x+a0f(x)=anxn+an–1xn–1+…+a1x+a0 is a polynomial.
∙ Now, a zero polynomial is a special case of the polynomial where all the coefficients an,an–1,an–2,……a1,a0 are zeros (0). Hence, the polynomial becomes f(x)=0 or the corresponding polynomial function is the constant function with value 0.
∙ f(x)=0, g(x)=0x, h(x)=0x2,p(x)=0x3, q(x)=0x12, r(x)=0x50
etc. are all examples of zero polynomials.
∙ 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.
The zero polynomial is considered as the additive identity of the polynomials.