Question

is the sum of two polynomials always a polynomial

Answer 1

What do you think is a polynomial?

Answer 2

yes .. but may be of two variables

Answer 3

f(x)=x^2
g(x)=-x^2

both are polynomials

f(x)+g(x)=0

Is 0 a polynomial? Yes, it is technically a polynomial of degree -1 or -infinity.

Answer 4

Addition of two polynomials will always yield a polynomial.
0 is a polynomial of zero degree.

Answer 5

A constant is a polynomial of zero degree. 0 is a polynomial of degree less than zero.

Answer 6

Don't you think 0 is a constant?