LOTS OF POINTS Part A:Create a 5th degree polynomial in standard form. How do you know it’s in standard form? Part B: Explain the

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LOTS OF POINTS
Part A:Create a 5th degree polynomial in standard form. How do you know it’s in standard form?
Part B: Explain the closure property as it relates to addition of polynomials. Give an example.​

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Trung Dũng 3 years 2021-09-03T18:18:03+00:00 1 Answers 27 views 0

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  1. Delwyn
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    2021-09-03T18:19:20+00:00
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    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:

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