Part A: Create an example of a 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. HELP PLEASE

Polynomial is basically the sum of terms, where each term is in the form of k·xⁿ ,where k is any constant and n is positive integer. If n becomes negative, it is not a Polynomial.

Example of Standard Form of Polynomial:

x³ + x² + x + 2

Why is it Standard form?

Standard form means that all the terms are ordered from the biggest exponent to the lowest exponent. We can write the given polynomial as:

As all the terms are ordered from the biggest exponent of x to the lowest exponent of x, it is a Standard Form of Polynomial

(3x+1) + (2x+5) = 5x+6

Variables and their exponents doesn't change, only the coefficients are added.

Polynomials are closed under Addition

(3x+1) - (2x+5) = x-4

Variables and their exponents doesn't change, only the coefficients are subtracted.

Polynomials are closed under Subtraction.

(x+1)(x-5) = x² - 5x + x + 5 = x² - 4x + 5

The exponents of variables are added, as newly formed exponents are also whole numbers, it fulfils the requirement for a polynomial.

Polynomials are closed under Multiplication

When dividing, there is a possibility of creating negative exponent, which is not allowed in polynomials.

Polynomials are NOT closed under Division

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.