Answer:
A. A fifth degree polynomial is defined by .
B. The closure property in relation to addition of polynomials is defined by following expression:
, ,
For and , we know that .
Step-by-step explanation:
A. A polynomial is in standard form if and only if is written in the following form:
, (1)
Where:
- Grade of the i-th monomial.
- Grade of the polynomial.
- i-th coefficient of the polynomial.
Then, a fifth degree polynomial in standard form is:
(3)
B. The closure property in relation to addition of polynomials is defined by following expression:
, , (3)
Let proceed to demonstrate this closure property for every polynomial:
1) Given.
2) Sum property/Associative property.
3) Sum property/Result.
Let consider that and , then we know by closure property for addition of polynomials that:
