Which example correctly demonstrates polynomial addition?(1 point)

To correctly demonstrate polynomial addition, we need to add the like terms from the two polynomials.

Let's simplify the expression \((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\):

1. Combine the \(x^2\) terms:
\[
2x^2 + 3x^2 = 5x^2
\]

2. Combine the \(x\) terms:
\[
6x + 3x = 9x
\]

3. Combine the constant terms:
\[
1 + 9 = 10
\]

Putting it all together, we get:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

So the correct answer is:
\((2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10\)

Which example correctly demonstrates polynomial subtraction?(1 point)

(2x^2+6x+1)−(3x^2+3x+9)=x^2+3x+8
(2x^2+6x+1)−(3x^2+3x+9)=5x^2+9x+10
(2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8
(2x^2+6x+1)−(3x^2+3x+9)=−5x^2+3x−8

To correctly demonstrate polynomial subtraction, we must subtract each term in the second polynomial from the corresponding term in the first polynomial.

Let's simplify the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\):

1. Subtract the \(x^2\) terms:
\[
2x^2 - 3x^2 = -x^2
\]

2. Subtract the \(x\) terms:
\[
6x - 3x = 3x
\]

3. Subtract the constant terms:
\[
1 - 9 = -8
\]

Putting it all together, we get:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]

So the correct answer is:
\((2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8\)

What does it mean for a set to be "closed"?(1 point) Responses An expression belonging to a closed set cannot be used to create an expression that is not of that set. An expression belonging to a closed set cannot be used to create an expression that is not of that set. An operation performed on members of that set will result in a member of the same set. An operation performed on members of that set will result in a member of the same set. Members of a closed set cannot be added, subtracted, multiplied, or divided. Members of a closed set cannot be added, subtracted, multiplied, or divided. The set has a finite number of members, as opposed to being infinitely large.

The correct response that defines what it means for a set to be "closed" is:

**An operation performed on members of that set will result in a member of the same set.**

In mathematical terms, a set is said to be closed under a particular operation (such as addition, subtraction, multiplication, or division) if performing that operation on any members of the set will always produce a result that is also a member of the set. For example, the set of integers is closed under addition since the sum of any two integers is always an integer.