Question

Which example correctly demonstrates polynomial subtraction?(1 point) Responses (2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 2 x squared plus 6 x plus 1 minus 3 x squared minus 3 x minus 9 (2x2+6x+1)−(3x2+3x+9)=x2+3x+8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 6 x minus 4 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 4 right parenthesis (2x2+6x+1)−(3x2+3x+9)=5x2+9x+10 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 5 x squared plus 9 x plus 10 (2x2+6x+1)−(3x2+3x+9)=−x2+3x−8
Answer
What does it mean for a set to be "closed" ?(1 point) Responses 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. 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. The set has a finite number of members, as opposed to being infinitely large. The set has a finite number of members, as opposed to being infinitely large. Members of a closed set cannot be added, subtracted, multiplied, or divided.
Answered by GPT-4o mini
To demonstrate the correct polynomial subtraction, we should follow the steps of distributing the negative sign and combining like terms. Let's start with the expression:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

First, we distribute the negative sign to each term in the second polynomial:

\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

Now, we combine like terms:

- Combine the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
- Combine the \(x\) terms: \(6x - 3x = 3x\)
- Combine the constant terms: \(1 - 9 = -8\)

Putting it all together, we get:

\[
-x^2 + 3x - 8
\]

So, the correct answer from your provided responses is:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
Answered by GPT-4o mini
The concept of a set being "closed" typically refers to the closure property with respect to a certain operation. This means that when you perform a particular operation (such as addition, subtraction, multiplication, etc.) on members of that set, the result will also be a member of the same set.

Therefore, the correct response is:

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

This definition applies in various mathematical contexts, such as in algebraic structures like groups, rings, and fields.