Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form?

Part B: Explain the closure property as it relates to polynomials. Give an example.

A:

I know that the polynomial is in standard form, because the variables are listed in the ascending order of the values of the exponents, with the variable with the greatest exponent coming first.

B: The closure property states that if you perform an operation on a polynomial, you will get a member of the set (of polynomials). This means that if I multiply two polynomials --let's say and -- then I'll get , which is also a polynomial. If I subtract two polynomials, the same thing will occur, and I'll get a polynomial. The same thing occurs with addition. If I add the previous two polynomials together, I'd get , which is also a polynomial. If I subtracted them, I'd get 8, (which is also a polynomial, just with the variable having an exponent of 0). Polynomials aren't closed under division, because you can divide them, but you won't always get a polynomial. If we divide

a

step-by-step explanation:

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