Question

Is the difference of two polynomials always a polynomial? Explain.

Answer 1

@Lilith

Answer 2

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

Answer 3

?

Answer 4

the two expressions are polynomials rite?

Answer 5

yes

Answer 6

but subtracting the second from the first, gives us an integer, which is not a polynomial. This is a counter example

Answer 7

so the answer is

Answer 8

It is shown that it's no.

Answer 9

actually it is yes

Answer 10

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

Answer 11

well, it seems so...though that would means any expression is a polynomial as long as the degree is a positive integer

Answer 12

f(x)=0
f(x)=-3
are both polynomials

to get the definition of polynomial:
http://en.wikipedia.org/wiki/Polynomial

Answer 13

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