Question

Select the correct answer.

Answer 1

Answer:

B.

f(x) and g(x) are closed under subtraction because when subtracted, the result will be a polynomial.

Step-by-step explanation:

$f(x)-g(x)\\=(a_0+a_1x+a_2x^2...+a_nx^n)-(b_0+b_1x+b_2x^2...b_mx^m)$

Assume m>=n WOLOG

$=(a_0-b_0)+(a_1x-b_1x)+(a_2x^2-b_2x^2)+...+(a_nx^n-b_nx^n)-b_{(n+1)}x^{n+1}-...-b_{m-1}x^{m-1}-b_mx^m$

$=(a_0-b_0)+(a_1-b_1)x+(a_2-b_2)x^2+...+(a_n-b_n)x^n-b_{(n+1)}x^{n+1}-...-b_{m-1}x^{m-1}-b_mx^m$

Are also a polynomial in general, but maybe in a different degree

Closure under subtraction means, for all polynomials, under the operation of subtraction, it also belongs to polynomials