The operation is a closed system under subtraction because subtracting one polynomial from another results in another polynomial of the same degree and type. In this case, subtracting \( (2x^2 + 12x + 11) \) from \( (9x^2 + 17x + 13) \) yields \( (9x^2 - 2x^2) + (17x - 12x) + (13 - 11) = 7x^2 + 5x + 2 \), which is still a polynomial.
In 1–2 sentences, explain why the following operation is a closed system under subtraction.
(9x^2+17x+13)−(2x^2+12x+11) (2 points) explain
3 answers
answer the question explain why the following operation is a closed system under subtraction.
(9x^2+17x+13)−(2x^2+12x+11)
(9x^2+17x+13)−(2x^2+12x+11)
The operation is a closed system under subtraction because subtracting one polynomial from another results in another polynomial. In this case, subtracting \( (2x^2 + 12x + 11) \) from \( (9x^2 + 17x + 13) \) produces \( (9x^2 - 2x^2) + (17x - 12x) + (13 - 11) = 7x^2 + 5x + 2 \), which is still a polynomial of the same type. Since the set of polynomials is closed under subtraction, this operation does not produce any results outside of that set.