In 1–2 sentences, explain why the following operation is a closed system under subtraction. (9x^2+17x+13)-(2x^2+12x+11)

Answer 1

The operation is a closed system under subtraction because subtracting any polynomial from another polynomial results in another polynomial, maintaining the set of polynomials as a whole. Specifically, the difference of the two given polynomials, \( (9x^2 + 17x + 13) - (2x^2 + 12x + 11) \), results in a polynomial \( (7x^2 + 5x + 2) \) which is still within the realm of polynomial functions.