Question

(06.01, 06.02 HC) I WILL MARK YOU BRAINIEST Part A: Create a fourth-degree polynomial in standard form. How do you know it is in standard form? (5 points) Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)

Answer 1

Part A:

A fourth-degree polynomial in standard form is :

• To write a polynomial in a standard form you have to set its terms according to the variable powers in a descending order.

       In this example it would give:

      −6$x^{4}$+3$x^{2}$+4x +2

• The degree of a polynomial is the maximum power of an unknown variable in the polynomial.

Part B:

The closure property as it relates to polynomials are :

• Polynomials are closed for addition and subtraction. This is because the power does not change.

• Only the coefficients are changed.

• This is illustrated by the examples below:

       (2x2 + 3x + 4) + (x2 - 5x - 3)

        3x2 - 2x + 1.

• The above operation does not change  the degree. Only the number next to each variable changes.

Therefore, the addition and subtraction of polynomials is closed.

Know more about polynomials:

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