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:

Analyze the closure property of polynomial addition

The closure property states that performing an operation (addition) on two elements of a set (polynomials) always results in an element that is also in that same set. Therefore, the sum of two polynomials is a polynomial.

Analyze the commutative property of polynomial addition

The commutative property states that the order in which terms are added does not affect the final result. Therefore, changing the order of two or more terms does not change the value of the sum.

Analyze the associative property of polynomial addition

The associative property states that the grouping of terms in an addition operation does not affect the final result. Therefore, the way in which two or more terms are grouped in a sum does not change the value.

Answer:

What do the properties of polynomial addition mean? Complete each statement.
The closure property states that the sum of two polynomials is a <blank>polynomial</blank>.
The commutative property states that changing the order of two or more terms <blank>does not change</blank> the value of the sum.
The associative property states that the way in which two or more terms are grouped in a sum <blank>does not change</blank> the value.