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take this \(x^2 +x+2\) and \(x^2 +x+4\) are their difference a polynomial?

the two expressions are polynomials rite?

yes

so the answer is

It is shown that it's no.

actually it is yes

Hmm ... I believe that integers are polynomials. An integer is simply a polynomial of degree zero.

degree is non-negative, so it can be 0 degree