Question

Select the correct answer.Let f(x) and g(x) be polynomials as shown below.f(x) = a + a₁ + a₂²... + anng(x) = bo + b₁x + b₂x² ... + bmxmWhich of the following is true about f(x) and g(x)?OA.OB.OC.O D.x) and g(x) are not closed under addition because when added, the result will not be a polynomial.(x) and g(x) are closed under addition because when added, the result will be a polynomial.x) and g(x) are closed under addition because when added, the result will not be a polynomial.f(x) and g(x) are not closed under addition because when added, the result will be a polynomial.

Answer 1

Step 1

Given; Select the correct answer.

Let f(x) and g(x) be polynomials as shown below.

f(x) = a + a₁ + a₂²... + aₙn

g(x) = bo + b₁x + b₂x² ... + bmxm

Which of the following is true about f(x) and g(x)?

Step 2

Polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Thus,

`f(x)+g(x)=(a_o+b_o)+(a_1+b_1)x+(a_2+b_2)x^2+....+(a_nx_(^n)+b_mx^m)`

As seen above, f(x) and g(x) are closed under addition because when added, the result will be a polynomial.

Answer; f(x) and g(x) are closed under addition because when added, the result will be a polynomial.