Question

1. if you add two polynomial functions, are they always a polynomial, or are they sometimes a polynomial, never a polynomial.

2. if you subtract two polynomial functions, are they always a polynomial, or are they sometimes a polynomial, never a polynomial.

EX: F(X) + G(X)
F(X) - G(X)

Answer 1

They are always polynomial.

Explanation:

adding , multiplying and subtracting polynomial function from another polynomial function always results polynomial. but you need to restrict the domain of the denominator function when you divide polynomial by another polynomial. it may not always result polynomial function.