Part a: create an example of a 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.

part a : a polynomial is in standard form if 1. the exponents of x are descending 2. no negative exponents for x example: x^2 + x + 3

part b : the closure property polynomials are 'closed' under addition and multiplication because if you add two polynomials, or multiply two polynomials , you get another polynomial.

example: suppose we are given the polynomials 3x2+2x+7 and 4x+1.

if we add them we get

(3x2+2x+7)+(4x+1)=3x2+6x+8

the sum is a polynomial. this is an example of closure of polynomials under addition.

if we multiply them we get

(3x2+2x+7)⋅(4x+1)=12x3+11x2+30x+7

the product is a polynomial. this is an example of closure of polynomials under multiplication.

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