The option (D) "f(x) and g(x) are closed under the addition because when added, the result will be a polynomial is correct.
What is polynomial?
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have given two polynomials:
[tex]\rm f(x) = \rm a_0+a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
[tex]\rm g(x) = \rm b_0+b_1x+b_2x^2+b_3x^3+b_4x^4..........b_mx^m[/tex]
If we add the above two polynomials:
= f(x) + g(x)
[tex]= (\rm a_0+a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n) + (\rm \rm b_0+b_1x+b_2x^2+b_3x^3+b_4x^4..........b_mx^m)[/tex]
The above expression is also a polynomial.
Thus, the option (D) "f(x) and g(x) are closed under the addition because when added, the result will be a polynomial is correct.
Learn more about Polynomial here:
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