Is zero a polynomial? Explain.?

Yes - you might or might not know that polynomials are related to vectors in that they form a vector space over a given field (real numbers, complex, mod n etc). All vector spaces have an element, let's call id(x) such that g(x) + id(x) = g(x); that is there exists the additive identity which, added to another element outputs the same element (in the real numbers, 1 + 0 = 1, so 0 is the additive element). In this case, id(x) = 0, so zero must be a polynomial. Another way to reconcile this with linear algebra is that every vector space must contain the zero vector (or in this case polynomial), and so p(x) = 0 is indeed a polynomial - if zero was NOT a polynomial, then a crucial vector space axiom - that the additive identity v + 0 = v exists - fails and it cannot be a vector space which is certainly untrue.

Without bringing linear algebra into this explanation, you can imagine zero as being a polynomial of undefined order - since any order polynomial with all coefficients equal to zero results in the zero polynomial. There are no restrictions on what the coefficients are for a polynomial (such as that they cannot be all trivial) so zero is a polynomial.

It depends on the way 0 is expressed.

Usually, a polynomial consists of the sum of at least two terms of the same variable. They may usually contain different powers, but must also have those powers as integers. Most polynomials require that the coefficients of the variable must be rational.

In the case of 0, it is rational. It could express the constant term or the coefficient when the variable of the power 0. Being only the constant, it is only one term, not following a rule of a polynomial. However, 0 can be written as the coefficient of several other variable powers. This makes the sum 0.

From the answer yes, see how it is possible.

Polynomial: 0x^3 + 0

This does look like a polynomial.

However, it might be questioned whether the zero you wrote is one term, or the sum. If the answer is no, it is probably because zero is that of a one-term monomial (not polynomial), not a sum.

Since there are several ways to sum zero in a polynomial even without 0 as a coefficient (when terms of common power have opposite signs), you can always simplify the polynomial and make it say 0.

x^2 - 3x + x + 2x - x^2 = zero

The argument holds yes if zero is meant to be a sum.

It is also possible to say no because of the numerous ways zero can be expressed as a non-polynomial. Another type of equation can have zero coefficients or zero as a sum.

02^x + 0x + 0|x|

3x - 3^x - 2x + 3^x - x

This argument holds no if zero is not taken as a sum of polynomial terms.

It mostly holds the answer to yes, but only if zero is taken as a sum.

a polynomial is an algebraic expression with more than one term. Zero if considered as a term is still just one term and cannot be a polynomial

YES. IT IS

NB: It is a polynomial but it is not a proper polynomial

NO.

zero by itself doesn't exists.

its nothing, not even a monomial.

how many terms are there in f(x) if f(x) = ?

no.