The operation is a closed system under subtraction because subtracting any two polynomials (like \(9x^2 + 17x + 13\) and \(2x^2 + 12x + 11\)) results in another polynomial, thereby ensuring that the set of polynomials is preserved under this operation. In this case, subtracting the second polynomial from the first yields another polynomial: \( (9x^2 - 2x^2) + (17x - 12x) + (13 - 11) = 7x^2 + 5x + 2\).
In 1–2 sentences, explain why the following operation is a closed system under subtraction (9x^2+17x+13)−(2x^2+12x+11)
9 answers
make it different
The operation is considered a closed system under subtraction because the difference between any two polynomials results in another polynomial, which remains within the same set of polynomial expressions. For instance, performing the subtraction \( (9x^2 + 17x + 13) - (2x^2 + 12x + 11) \) yields \( 7x^2 + 5x + 2 \), confirming that the outcome is still a polynomial.
more different?
The subtraction of the two polynomials, \( (9x^2 + 17x + 13) - (2x^2 + 12x + 11) \), is closed because the resulting expression, \( 7x^2 + 5x + 2 \), adheres to the structure of a polynomial. Since the operation doesn't lead to an expression outside the polynomial realm, it confirms that the set of polynomials remains complete under the subtraction operation.
more different plz?
The operation of subtracting the polynomial \( (2x^2 + 12x + 11) \) from \( (9x^2 + 17x + 13) \) stays within the realm of polynomials, meaning it maintains closure. This is evident as the resulting polynomial, \( 7x^2 + 5x + 2 \), is still a polynomial, thus confirming that the set of polynomials is unaffected by the subtraction operation.
make it more different
The subtraction of the polynomial \( (2x^2 + 12x + 11) \) from \( (9x^2 + 17x + 13) \) exemplifies a closed operation within the space of polynomials because it produces another polynomial as a result. Specifically, this process demonstrates that performing algebraic operations on polynomials consistently yields results that belong to the same category, ensuring the integrity of the polynomial set is preserved.
1 answer