The subtraction of two polynomials results in another polynomial, hence polynomials are closed under subtraction, making option D correct.
The correct answer to the given question is D. f(x) and g(x) are closed under subtraction because when subtracted, the result will be a polynomial.
Polynomials are closed under subtraction, which means that the subtraction of two polynomials is also a polynomial.
This can be seen by subtracting the polynomial g(x) from f(x), where you would subtract the corresponding coefficients of like terms.
Even if the polynomials are of different degrees (where n might not equal m), the highest degree of the resulting polynomial will be at most the larger of the two degrees (either n or m).
The probable question may be:
Let f(x) and g(x) be polynomials as shown below.
f(x)=a_0+a_1x + a_2x^2 ..+a_nx^n
g(x)=b_0+b_1x+b_2x^2 ...+b_mx^m
Which of the following is true about f(x) and g(x)
A, f(x) and g(x) are closed under subtraction because when subtracted, the result will not be a polynomial..
B. f(x) and g(x) are not closed under subtraction because when subtracted, the result will not be a polynomial.
C. f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial.
D. f(x) and g(x) are closed under subtraction because when subtracted, the result will be a polynomial.