Question

describing the properties of polynomial addition. what do the properties of polynomial addition mean? complete each statement. the closure property states that the sum of two polynomials is a. the commutative property states that changing the order of two or more terms the value of the sum. the associative property states that the way in which two or more terms are grouped in a sum the value.

Explanation:

1. The closure property of polynomial addition means that when you add two polynomials, the result is always a polynomial.
2. The commutative property of addition (including for polynomials) states that for any two terms \(a\) and \(b\), \(a + b=b + a\), so changing the order of terms does not change the sum's value.
3. The associative property of addition (for polynomials too) says that for any three terms \(a\), \(b\), and \(c\), \((a + b)+c=a+(b + c)\), so the way terms are grouped does not change the sum's value.

Answer:

The closure property states that the sum of two polynomials is a polynomial.
The commutative property states that changing the order of two or more terms does not change the value of the sum.
The associative property states that the way in which two or more terms are grouped in a sum does not change the value.