Is it possible to add 2 polynomials together and your answer not be a polynomial? Provide an example and an explanation ?

Question

anonymous · Answer

Yes, for instance 

x^2 + 2x + 4 +  -x^2 + -2x + 4

x^2 -x^2  + 2x -2x  + 4 + 4 =  8  

8 is not a poly

lyrae · Answer

@MDoodler 8 is a polynomial of degree 0. f(x) = 8*x^0 is graphed as a line. Also note that f(x) = 0 is called the zero-polynomial and is hence also a polynomial. Adding or subtracting polynomials will in fact always result in a new polynomial. http://www.oxfordmathcenter.com/drupal7/node/553

lyrae · Answer

$$f(x) = 8x^0, \space x \neq 0$$