Is the difference of two polynomials always a polynomial? Explain

Question

amistre64 · Answer

x^2-x^2 = 0, so no

hartnn · Answer

isn't 0 a polynomial ??

hartnn · Answer

@amistre64

hartnn · Answer

and yes, difference of 2 polynomials is always a polynomial.

hartnn · Answer

same as addition,multiplication or division.

anonymous · Answer

A polynomial is just a number expressed as a sum of one or more terms.
e.g. 1243 = 1000+200+40+3 = 1x10^3 +2x10^2 +4x10^1 +3x10^0.

As long as your polynomial has real coefficients, then all the operations should be valid (still no dividing by zero, though)

anonymous · Answer

The answer depends on the two polynomials. If both polynomials have different like terms, than how will the polynomials be subtracted?

hartnn · Answer

0 is indeed a polynomial.
the degree of zero polynomial p(x)=0 is $-\infty$.

amistre64 · Answer

http://mathworld.wolfram.com/ConstantPolynomial.html i must have been confusing it with the "first coefficient" requirement to be non zero