Question

Is it possible to add 2 polynomials together and your answer is not a polynomial? Please provide an example and an explanation

Answer 1

Polynomials are "closed" under addition. This means all polynomials, when added to other polynomials, will always produce polynomials. Notice how when you add polynomials, the exponents never change (just constants and coefficients) so you can never turn positive integer exponents into non-positive/non-integer exponents.

It says to ask for an example, so you could just make up two polynomials like... idk 2x^2 + 3x + 5 and x^4 + 2 and show how the result is also a polynomial.

Answer 2

I can think of a special case when the two polynomials are same with opposite coefficients and any constant value.
Exmple:
ax^2 + bx + c and -ax^2 - bx + d
Adding up the above will give us c + d which is a constant value and not a polynomial.